Hypothesis Tests Chapter 4 Test Bank Answers - Download Test Bank | Unlocking Statistics 3e by Robin H. Lock. DOCX document preview.
Statistics - Unlocking the Power of Data, 3e (Lock)
Chapter 4 Hypothesis Tests
4.1 Introducing Hypothesis Tests
1) The p-value is
A) the probability that the null hypothesis is true.
B) the probability that the alternative hypothesis is true.
C) the probability, when the null hypothesis is true, of obtaining a sample as extreme as (or more extreme than) the observed sample.
D) the probability, when the alternative hypothesis is true, of obtaining a sample as extreme as (or more extreme than) the observed sample.
Diff: 2 Type: MC Var: 1
L.O.: 4.2.1
2) The following figure shows a randomization distribution for the hypotheses versus The statistic used for each sample is Which of the two possible sample results provides the most evidence against ?
A) = 56.5; = 51.3
B) = 50.2; = 53.1
Diff: 1 Type: MC Var: 1
L.O.: 4.1.3
3) The average SAT-Critical Reading score for college bound students taking the exam in the 2018-2019 academic year was 501 531. A highly selective university wants to know if their 2020 incoming class had an average SAT-Critical Reading score that was higher than the national average. Which of the following possible samples provides the most evidence for this claim?
A) Sample A
B) Sample B
C) Sample C
D) Sample D
Diff: 1 Type: BI Var: 1
L.O.: 4.1.3
4) A statistical test uses data from a sample to assess a claim about a population.
Diff: 2 Type: TF Var: 1
L.O.: 4.1.1
5) Identify the error in the following hypotheses: versus
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2
6) Identify the error in the following hypotheses: of versus
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2
7) Identify the error in the following hypotheses: versus
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2
8) Which of the following samples provides the most evidence that the amount of time spent studying for an exam and the grade on the exam are positively correlated?
A) Sample A
B) Sample B
C) Sample C
D) Sample D
Diff: 2 Type: BI Var: 1
L.O.: 4.1.3
Use the following to answer the questions below:
A study described in Attention, Perception, and Psychophysics investigated the impacts of multi-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition" for both people who play video games and those who do not.
9) What does the phrase "significantly worse" mean in this context?
Diff: 2 Type: ES Var: 1
L.O.: 4.1.4
4.2 Measuring Evidence with P-values
1) Of the two p-values, which provides more evidence against ?
A) p-value = 0.49
B) p-value = 0.007
Diff: 1 Type: MC Var: 1
L.O.: 4.2.4
Use the following to answer the questions below:
Consider testing the hypotheses : p = 0.4 versus : p > 0.4. Four possible sample statistics, along with four possible p-values, are given. Match the statistics to their p-values.
A = 0.42 B = 0.38 C = 0.51 D = 0.46
2) ________ p-value = 0.72
Diff: 2 Type: SA Var: 1
L.O.: 4.2.1
3) ________ p-value = 0.293
Diff: 2 Type: SA Var: 1
L.O.: 4.2.1
4) ________ p-value = 0.138
Diff: 2 Type: SA Var: 1
L.O.: 4.2.1
5) ________ p-value = 0.019
Diff: 2 Type: SA Var: 1
L.O.: 4.2.1
6) The randomization distribution for testing the hypotheses versus is provided. The sample statistic is Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this test.
Diff: 2 Type: SA Var: 1
L.O.: 4.2.2
7) The provided figure displays the randomization distribution for testing versus
The p-value for the sample mean = 112 is closest to
A) 0.01
B) 0.25
Diff: 2 Type: BI Var: 1
L.O.: 4.2.2
8) Decreasing the significance level of a hypothesis test (say, from 5% to 1%) will cause the p-value of an observed test statistic to
A) increase.
B) decrease.
C) stay the same.
Diff: 3 Type: BI Var: 1
L.O.: 4.2.1;4.2.3
9) Using the definition of a p-value, explain why the area in the tail of a randomization distribution is used to compute a p-value.
Diff: 2 Type: ES Var: 1
L.O.: 4.2.1;4.2.3
4.3 Determining Statistical Significance
1) A Type I error occurs by
A) rejecting the null hypothesis when the null hypothesis is false.
B) not rejecting the null hypothesis when the null hypothesis is false.
C) rejecting the null hypothesis when the null hypothesis is true.
D) not rejecting the null hypothesis when the null hypothesis is true.
Diff: 2 Type: BI Var: 1
L.O.: 4.3.3
2) A Type II error occurs by
A) rejecting the null hypothesis when the null hypothesis is false.
B) not rejecting the null hypothesis when the null hypothesis is false.
C) rejecting the null hypothesis when the null hypothesis is true.
D) not rejecting the null hypothesis when the null hypothesis is true.
Diff: 2 Type: BI Var: 1
L.O.: 4.3.3
3) Using a significance level of 5%, the appropriate conclusion for a test with a p-value of 0.0421 would be:
A) Reject
B) Do not reject
Diff: 1 Type: BI Var: 1
L.O.: 4.3.1
4) The significance level, α, represents the tolerable probability of making a Type II error.
Diff: 2 Type: TF Var: 1
L.O.: 4.3.4
Use the following to answer the questions below:
Match each p-value to the most appropriate conclusion.
A 0.0001 B 0.0735 C 0.6082 D 0.0361
5) ________ "The evidence against the null and in favor of the alternative is very strong."
Diff: 2 Type: SA Var: 1
L.O.: 4.3.1
6) ________ "The result is significant at the 5% level but not at a 1% level."
Diff: 2 Type: SA Var: 1
L.O.: 4.3.1
7) ________ "There is really no evidence supporting the alternative hypothesis."
Diff: 2 Type: SA Var: 1
L.O.: 4.3.1
8) ________ "The evidence against the null is significant, but only at the 10% level."
Diff: 2 Type: SA Var: 1
L.O.: 4.3.1
Use the following to answer the questions below:
A study described in Attention, Perception, and Psychophysics investigated the impacts of multi-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition" for both people who play video games and those who do not.
9) What conclusion would the authors have made at the 10% significance level?
A) Tracking accuracy was significantly worse in the dual-task condition.
B) Tracking accuracy was not significantly worse in the dual-task condition.
C) Not enough information
Diff: 3 Type: MC Var: 1
L.O.: 4.3.1
10) What conclusion would the authors have made at the 1% significance level?
A) Tracking accuracy was significantly worse in the dual-task condition.
B) Tracking accuracy was not significantly worse in the dual-task condition.
C) Not enough information
Diff: 3 Type: MC Var: 1
L.O.: 4.3.1
11) Which type of error, Type I or Type II, could have occurred in this situation? Briefly justify your answer.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.3
4.4 A Closer Look at Testing
1) It is of interest to test the hypotheses : p = 0.8 versus The sample outcome, based on observations, is and the randomization statistic to be calculated is . The p-value for this test was found to be 0.322. If the test was performed correctly, where should the randomization distribution be centered?
A) 0.7
B) 10
C) 0.8
D) 0.322
Diff: 1 Type: BI Var: 1
L.O.: 4.4.1
2) It is believed that about 37% of college students binge drink (5 or more drinks for men, and 4 or more drinks for women, in two hours). Administrators at a small university of 6,000 students want to do a study to determine if the proportion of their students who binge drink differs from 37%. They select a sample of 98 students enrolled at the university to survey about their drinking behavior. When generating the randomization distribution for this test, how large should each individual randomization sample be?
A) 98 because that is the size of the original sample
B) 1,000 to get an accurate randomization distribution
C) 6,000 because that is the size of the university
D) 2,220 because that is 37% of the students at the university
Diff: 2 Type: BI Var: 1
L.O.: 4.4.1
3) When generating a randomization sample, the sample should be consistent with the ________ hypothesis.
Diff: 1 Type: SA Var: 1
L.O.: 4.4.1
4) The null and alternative hypotheses for a test are vs. Give the notation for a sample statistic we might record for each simulated sample to create the randomization distribution.
A)
B) p
C) μ
D)
Diff: 2 Type: BI Var: 1
L.O.: 4.4.1
Use the following to answer the questions below:
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.
Green | Not Green | Total | |
Milk Chocolate | 8 | 33 | 41 |
Dark Chocolate | 4 | 38 | 42 |
Total | 12 | 71 | 83 |
5) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
If the null hypothesis were true, green candies would be equally likely to appear in either bag. Since there are 83 candies, we should construct a deck of 83 cards - 12 of which are green (representing the 12 total green candies she observed) and the rest can be white (representing the "other" colors she observed). We would shuffle the deck and deal out two piles (one with 41 cards to represent the Milk Chocolate candies and the other with 42 cards to represent the Dark Chocolate candies). From those samples we could record the difference in the sample proportions of green candies:
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
6) Use the provided randomization distribution (based on 100 samples) to test if this sample provides evidence that the proportion of candies that are green differs for the two types of M&M's. Include an assessment of the strength of your evidence.
Parameters: = the proportion of milk chocolate candies that are green and = the proportion of dark chocolate candies that are green
Hypothesis: : = versus : ≠
The sample difference in proportions is - = 8/41 - 4/42 = 0.195 - 0.095 = 0.10.
In the randomization distribution, 16 dots of the 100 (16/100) dots greater than or equal to 0.10. However, since this is a two-sided test, this must be multiplied by 2 to obtain the correct p-value:
This p-value provides no evidence that the proportion of green candies differs for milk chocolate and dark chocolate M&M's.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.4
7) Use technology and the provided data to test if this sample provides evidence that the proportion of candies that are green differs for the two types of M&M's. Include an assessment of the strength of your evidence.
Parameters: = the proportion of milk chocolate candies that are green and = the proportion of dark chocolate candies that are green
Hypothesis: : = versus
The sample difference in proportions is - = 8/41 - 4/42 = 0.195 - 0.095 = 0.10.
The actual p-value for this test will vary depending upon the student's randomization distribution, but it should be somewhere near 0.13. They should be providing a two-sided p-value.
Their conclusion should be consistent with their p-value (and either a formal decision based on a significance level or an informal statement of the strength of their evidence against the null). Most p-values should lead the students to fail to reject the null hypothesis and conclude that this sample does not provide evidence that the proportion of green candies differs for the two types of M&M's.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.3; 4.4.4
Use the following to answer the questions below:
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.
Green | Not Green | Total | |
Milk Chocolate | 8 | 33 | 41 |
Dark Chocolate | 4 | 38 | 42 |
Total | 12 | 71 | 83 |
8) Define the appropriate parameter(s) and state the hypotheses for testing if the proportion of green M&M's differs for milk chocolate and dark chocolate M&M's.
= proportion of milk chocolate M&M's that are green
= proportion of dark chocolate M&M's that are green
: =
: ≠
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2
9) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
10) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.2;4.4.3
11) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.2;4.3.5
Use the following to answer the questions below
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.
Green | Not Green | Total | |
Milk Chocolate | 8 | 33 | 41 |
Dark Chocolate | 4 | 38 | 42 |
Total | 12 | 71 | 8 |
12) Define the appropriate parameter(s) and state the hypotheses for testing if the proportion of green M&M's differs for milk chocolate and dark chocolate M&M's.
= proportion of milk chocolate M&M's that are green
= proportion of dark chocolate M&M's that are green
: =
: ≠
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2
13) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
14) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.2.2;4.4.2
15) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.2;4.3.5
Use the following to answer the questions below:
As of July 8, 2020, the national average price for a gallon of regular unleaded gasoline was $2.18. The prices for a sample of gas stations in the state of Illinois are provided.
$2.365 | $2.417 | $2.437 | $2.421 | $2.396 | $2.444 | $2.422 | $2.374 | $2.422 | $2.447 |
It is of interest to use this sample to compare the average gas price in Illinois to the national average.
16) Describe how you could generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
The student should first notice a couple of things:
1) The sample mean is $2.415.
2) Since the parameter (average gas price in Illinois) is going to be compared to the "national average", the null hypothesis should state that
The original sample needs to be consistent with the null hypothesis, so all observations in the sample should be subtracted by 2.415-2.18 making the sample mean now 2.18 (i.e., preserving the general structure of the original sample but making it consistent with the null hypothesis). We could write each new sample value on an index card, shuffle the cards, select one, record that value, replace that card in the deck, and repeat (sampling with replacement) until we have a new sample of size 10 that is consistent with the null hypothesis (yet still preserves the structure of the original sample). We would then record the sample mean, , from this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
17) Use the provided randomization distribution (based on 1,000 samples) to test if this sample provides evidence that the average gas price in Illinois exceeds the national average. Include an assessment of the strength of your evidence.
Parameter: μ = average gas price in Illinois
Hypotheses: : μ = 2.18 versus : μ > 2.18
The sample statistic based on the original sample is = 2.415.
None of the dots in the dotplot of the randomization distribution exceed (or are equal to) the sample mean, so the p-value for this test is 0.
This p-value provides very strong evidence that the average gas price in Illinois is greater than 2.18 (the national average).
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.4
18) Use technology and the provided data to test if this sample provides evidence that the average gas price in Illinois exceeds the national average. Include an assessment of the strength of your evidence.
Parameter: μ = average gas price in Illinois
Hypotheses: μ = 2.18 versus : μ > 2.18
The sample statistic based on the original sample is = 2.415.
The actual p-value will vary for the students, but they should be counting the number of dots that correspond to sample statistics greater than or equal to the observed 2.415 (which will likely be zero or very small).
Their conclusion should be consistent with their p-value (and they will likely find very strong evidence that the average gas price in Illinois exceeds the national average).
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.3; 4.4.4
Use the following to answer the questions below:
As of July 8, 2020, the national average price for a gallon of regular unleaded gasoline was $2.18. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.
$2.365 | $2.417 | $2.437 | $2.421 | $2.396 | $2.444 | $2.422 | $2.374 | $2.422 | $2.447 |
It is of interest to use this sample to compare the average gas price in Illinois to the national average.
19) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average gas price in Illinois exceeds the national average.
A) Parameter: μ = average gas price in Illinois
Hypotheses: : μ = 2.18 versus : μ > 2.18
B) Parameter: μ = average gas price in Illinois
Hypotheses: : μ = 2.18 versus : μ ≠ 2.18
C) Parameter: μ = average gas price in Illinois
Hypotheses: : μ > 2.18 versus : μ = 2.18
D) Parameter: μ = average gas price in Illinois
Hypotheses: : μ ≠ 2.18 versus : μ = 2.18
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
20) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
1) The sample mean is $3.975.
2) Since the parameter (average gas price in Illinois) is going to be compared to the "national average," the null hypothesis should state that
The original sample needs to be consistent with the null hypothesis, so all observations in the sample should be subtracted by , making the sample mean now 2.18 (i.e., preserving the general structure of the original sample but making it consistent with the null hypothesis). We could write each new sample value on an index card, shuffle the cards, select one, record that value, replace that card in the deck, and repeat (sampling with replacement) until we have a new sample of size 10 that is consistent with the null hypothesis (yet still preserves the structure of the original sample). We would then record the sample mean, , from this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
21) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.3
22) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.2;4.3.5
Use the following to answer the questions below:
As of July 8, 2020, the national average price for a gallon of regular unleaded gasoline was $2.18. The prices for a sample of gas stations in the state of Illinois are provided.
$2.365 | $2.417 | $2.437 | $2.421 | $2.396 | $2.444 | $2.422 | $2.374 | $2.422 | $2.447 |
It is of interest to use this sample to compare the average gas price in Illinois to the national average.
23) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average gas price in Illinois exceeds the national average.
A) Parameter: μ = average gas price in Illinois
Hypotheses: : μ = 2.18 versus : μ > 2.18
B) Parameter: μ = average gas price in Illinois
Hypotheses: : μ = 2.18 versus : μ ≠ 2.18
C) Parameter: μ = average gas price in Illinois
Hypotheses: : μ > 2.18 versus : μ = 2.18
D) Parameter: μ = average gas price in Illinois
Hypotheses: : μ ≠ 2.18 versus : μ = 2.18
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
24) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
1) The sample mean is $2.415.
2) Since the parameter (average gas price in Illinois) is going to be compared to the "national average", the null hypothesis should state that
The original sample needs to be consistent with the null hypothesis, so all observations in the sample should be subtracted by making the sample mean now 3.63 (i.e., preserving the general structure of the original sample but making it consistent with the null hypothesis). We could write each new sample value on an index card, shuffle the cards, select one, record that value, replace that card in the deck, and repeat (sampling with replacement) until we have a new sample of size 10 that is consistent with the null hypothesis (yet still preserves the structure of the original sample). We would then record the sample mean, , from this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
25) Use the provided randomization distribution (based on 1,000 samples) to estimate the p-value for this sample.
Diff: 2 Type: SA Var: 1
L.O.: 4.2.2
26) Use the provided randomization distribution (based on 1,000 samples) to estimate the p-value for this sample. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.2;4.3.5
27) The provided histogram displays the prices (in thousands of dollars) of 25 homes sold in 2019 in a Midwestern city.
In general, this shape, right skewed with some unusually high values, is common for describing home values in many cities. For this reason, the median home value for a city is a useful parameter. This sample of recently sold homes had a median price (value) of $232,500. Someone considering moving to this city is interested in knowing if the median home value is more than $200,000.
Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate from the sample.
Diff: 3 Type: ES Var: 1
L.O.: 4.4.0
Use the following to answer the questions below:
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is about 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
28) Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
29) Use the provided randomization distribution (based on 100 samples) to determine if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years. Use a 5% significance level to make your conclusion.
Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ = 130 versus : μ < 130
The observed sample statistic is 120 years.
To obtain the p-value we can count the number of dots at or below 120 (note that either 8 or 10 dots should be an acceptable answer). Thus, a p-value of either 0.08 or 0.10 would be acceptable.
This p-value would lead us to not reject the null hypothesis and conclude that there is little to no evidence that the average age of driftwood along this beach is less than 130 years old.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.1; 4.3.2; 4.4.4
Use the following to answer the questions below:
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
98 | 79 | 147 | 200 | 130 | 60 | 51 | 127 | 105 | 75 | 120 | 113 | 200 | 190 |
81 | 98 | 160 | 165 | 134 | 62 | 152 | 66 | 68 | 124 | 190 | 159 | 60 |
30) Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
31) Use technology and the provided data to determine if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years. Use a 5% significance level to make your conclusion.
Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ = 130 versus : μ < 130
The observed sample statistic is 119.037 years.
The p-value is 0.114.
Because 0.114 > 0.05, we would not reject the null hypothesis and thus we have no evidence to conclude that the average age of the driftwood on the beach is less than 130 years.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.5; 4.3.1; 4.3.2; 4.4.3; 4.4.4
Use the following to answer the questions below:
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is approximately 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
32) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years.
A) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ = 130 versus : μ < 130
B) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ = 130 versus : μ ≠ 130
C) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ ≠ 130 versus : μ = 130
D) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ > 130 versus : μ = 130
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
33) Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
34) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.2.2
35) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.1;4.3.2
36) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. What conclusion would you make at the 10% significance level?
Diff: 2 Type: ES Var: 1
L.O.: 4.3.1
Use the following to answer the questions below:
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
98 | 79 | 147 | 200 | 130 | 60 | 51 | 127 | 105 | 75 | 120 | 113 | 200 | 190 |
81 | 98 | 160 | 165 | 134 | 62 | 152 | 66 | 68 | 124 | 190 | 159 | 60 |
37) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years.
A) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ = 130 versus : μ < 130
B) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ = 130 versus : μ > 130
C) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ < 130 versus : μ = 130
D) Parameter: μ = average age of driftwood trees along this beach
Hypotheses: : μ > 130 versus : μ = 130
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
38) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
39) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.3
40) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.1;4.3.2
41) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. What conclusion would you make at the 10% significance level?
Diff: 2 Type: ES Var: 1
L.O.: 4.3.1
Use the following to answer the questions below:
There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university.
Male | 3 | 1 | 12 | 12 | 0 | 4 | 10 | 4 | 5 | 5 | 2 | 10 | 10 | = 6  |
Female | 10 | 3 | 2 | 10 | 3 | 2 | 0 | 1 | 6 | 1 | 5 | = 4  |
42) Does this sample provide evidence that, on average, male students watch more television than female students at this university? Describe how you could generate a single randomization sample in this situation, and identify the statistic that you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
43) Use technology to determine if this sample provides evidence that, on average, male students watch more television than female students at this university. Include an assessment of the strength of the evidence.
Parameters: = mean number of hours of television per week for male students and number of hours of television per week for female students
Hypotheses: : = versus : >
The observed difference in sample means was
P-values will vary, though they should be near 0.10.
Conclusions will vary but should convey that this sample provides little/no evidence that male students watch more television each week than female students at this university.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.3; 4.4.4
44) Use the provided randomization distribution (based on 100 samples) to determine if this sample provides evidence that, on average, male students watch more television than female students at this university. Include an assessment of the strength of the evidence.
Parameters: = mean number of hours of television per week for male students and number of hours of television per week for female students
Hypotheses: : = versus : >
The observed difference in sample means was
There are 10 (12 is also acceptable) dots greater than or equal to the observed difference of 2. The p-value is 10/100 = 0.10 (or 12/100 = 0.12).
This sample provides no evidence that male students watch more television each week than female students at this university.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.4
Use the following to answer the questions below:
There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university.
Male | 3 | 1 | 12 | 12 | 0 | 4 | 10 | 4 | 5 | 5 | 2 | 10 | 10 | = 6 |
Female | 10 | 3 | 2 | 10 | 3 | 2 | 0 | 1 | 6 | 1 | 5 | = 4 |
45) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that, on average, male students watch more television than female students at this university.
A) Parameters: = mean number of hours of television per week for male students and number of hours of television per week for female students
Hypotheses: : = versus : >
B) Parameters: = mean number of hours of television per week for male students and number of hours of television per week for female students
Hypotheses: : < versus : =
C) Parameters: = mean number of hours of television per week for male students and number of hours of television per week for female students
Hypotheses: : = versus : <
D) Parameters: = mean number of hours of television per week for male students and number of hours of television per week for female students
Hypotheses: : > versus : =
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
46) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
47) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.
There are 10 (12 is also acceptable) dots greater than or equal to the observed difference of 2. The p-value is (or
Diff: 2 Type: ES Var: 1
L.O.: 4.2.2
48) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
A) This sample provides no evidence that male students watch more television each week than female students at this university.
B) This sample provides strong evidence that male students watch more television each week than female students at this university.
Diff: 2 Type: BI Var: 1
L.O.: 4.3.2;4.3.5
Use the following to answer the questions below:
There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university.
Male | 3 | 1 | 12 | 12 | 0 | 4 | 10 | 4 | 5 | 5 | 2 | 10 | 10 | = 6 |
Female | 10 | 3 | 2 | 10 | 3 | 2 | 0 | 1 | 6 | 1 | 5 | = 4 |
49) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that, on average, male students watch more television than female students at this university.
Parameters: = mean number of hours of television per week for male students and number of hours of television per week for female students
Hypotheses: : = versus : >
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2
50) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
51) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.
P-values will vary, though they should be near 0.10.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.3
52) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
A) This sample provides no evidence that male students watch more television each week than female students at this university.
B) This sample provides strong evidence that male students watch more television each week than female students at this university.
Diff: 2 Type: BI Var: 1
L.O.: 4.3.2;4.3.5
Use the following to answer the questions below:
The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one-third of the city's households have pets (otherwise there won't be enough business). He samples 150 of the households and finds that 64 have pets.
53) Describe how you could generate a single randomization sample in this situation, and identify the statistic that you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
54) Use technology to determine if this sample provides evidence that more than one-third of households in this city own pets. Use a 5% significance level.
Parameter: p = proportion of households in this city with pets
Hypotheses: : p = 1/3 versus : p > 1/3
The observed sample statistic is
P-values will vary though it will be approximately 0.004.
Conclusion should be consistent with p-value, though it should convey that the sample provides pretty strong evidence to reject the null hypothesis (since and conclude that there is strong evidence that more than 1/3 of the households in this city have pets.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.1; 4.3.2; 4.4.3; 4.4.4
55) Use the provided randomization distribution (based on 100 samples) to determine if this sample provides evidence that more than one-third of households in this city own pets. Use a 5% significance level.
Parameter: p = proportion of households in this city with pets
Hypotheses: : p = 1/3 versus : p > 1/3
The observed sample statistic is (so the cut-off for counting is halfway between 0.40 and 0.45). There is only one dot at a value greater than or equal to 0.426. Thus, the p-value is 0.01.
This sample provides strong evidence (since to reject the null hypothesis and conclude that more than 1/3 of households in this city own pets.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.1; 4.3.2; 4.4.4
Use the following to answer the questions below:
The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one-third of the city's households have pets (otherwise there won't be enough business). He samples 150 of the households and finds that 64 have pets.
56) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that more than one-third of households in this city own pets.
A) Parameter: p = proportion of households in this city with pets
Hypotheses: : p = 1/3 versus : p > 1/3
B) Parameter: p = proportion of households in this city with pets
Hypotheses: : p < 1/3 versus : ≥ 1/3
C) Parameter: p = proportion of households in this city with pets
Hypotheses: : p = 1/3 versus : p ≠ 1/3
D) Parameter: p = proportion of households in this city with pets
Hypotheses: : p ≠ 1/3 versus : p = 1/3
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
57) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
58) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.
This sample provides strong evidence that more than 1/3 of households in this city own pets.
Diff: 2 Type: ES Var: 1
L.O.: 4.2.2
59) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
A) This sample provides strong evidence to reject the null hypothesis and conclude that more than 1/3 of households in this city own pets.
B) This sample does not provide enough evidence to reject the null hypothesis and we can not conclude that more than 1/3 of households in this city own pets.
Diff: 2 Type: BI Var: 1
L.O.: 4.3.1;4.3.2
Use the following to answer the questions below:
The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one-third of the city's households have pets (otherwise there won't be enough business). He samples 150 of the households and finds that 64 have pets.
60) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that more than one-third of households in this city own pets.
A) Parameter: p = proportion of households in this city with pets
Hypotheses: : p = 1/3 versus : p > 1/3
B) Parameter: p = proportion of households in this city with pets
Hypotheses: : p < 1/3 versus : ≥ 1/3
C) Parameter: p = proportion of households in this city with pets
Hypotheses: : p = 1/3 versus : p ≠ 1/3
D) Parameter: p = proportion of households in this city with pets
Hypotheses: : p ≠ 1/3 versus : p = 1/3
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
61) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
62) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.
P-values will vary though it will be approximately 0.004.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.3
63) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.1;4.3.2
Use the following to answer the questions below:
A Division III college men's basketball team is interested in identifying factors that impact the outcomes of their games. They plan to use "point spread" (their score minus their opponent's score) to quantify the outcome of each game this season; positive values indicate games that they won while negative values indicate games they lost. They want to determine if "steal differential" (the number of steals they have in the game minus the number of steals their opponent had) is related to point spread; positive values indicate games where they had more steals than their opponent. The data for the first five games are in the provided table as an example.
Point Spread (y) | Steal Differential (x) |
4 | 7 |
2 | -2 |
-21 | -2 |
-4 | 1 |
-9 | 2 |
 | |
The correlation between point spread and steal differential for the games they played this season is about Assuming that this season was a typical season for the team, they want to know if steal differential is positively correlated with point spread.
64) Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
65) Use the provided randomization distribution (based on 100 samples) to determine if this sample provides evidence that point spread and steal differential are positively correlated. Use a 10% significance level to make your conclusion.
Hypotheses: : ρ = 0 versus : ρ > 0
The sample statistic is r = 0.35. There are 6 dots corresponding to values greater than or equal to 0.35 (0.35 is located halfway between 0.30 and 0.40). Thus, the p-value is
The p-value is less than α = 0.10 (the significance level), thus this season provides some evidence that point spread and steal differential are positively correlated.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.1; 4.3.2; 4.4.4
Use the following to answer the questions below:
A Division III college men's basketball team is interested in identifying factors that impact the outcomes of their games. They plan to use "point spread" (their score minus their opponent's score) to quantify the outcome of each game this season; positive values indicate games that they won while negative values indicate games they lost. They want to determine if "steal differential" (the number of steals they have in the game minus the number of steals their opponent had) is related to point spread; positive values indicate games where they had more steals than their opponent. The data for the first five games are in the provided table as an example.
Point Spread (y) | Steal Differential (x) |
4 | 7 |
2 | -2 |
-21 | -2 |
-4 | 1 |
-9 | 2 |
| |
The correlation between point spread and steal differential for the games they played this season is about Assuming that this season was a typical season for the team, they want to test if this sample provides evidence that steal differential is positively correlated with point spread.
66) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that steal differential is positively correlated with point spread.
A) Parameter: ρ = correlation between point spread and steal differential for this team
Hypotheses: : : ρ = 0 versus : ρ > 0
B) Parameter: ρ = correlation between point spread and steal differential for this team
Hypotheses: : : ρ = 0 versus : ρ ≠ 0
C) Parameter: ρ = correlation between point spread and steal differential for this team
Hypotheses: : : ρ = 0 versus : ρ < 0
D) Parameter: ρ = correlation between point spread and steal differential for this team
Hypotheses: : : ρ < 0 versus : ρ = 0
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
67) Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
68) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.
A) The p-value is 0.06
B) The p-value is 0.35
C) The p-value is 0.12
D) The p-value is 0.14
Diff: 2 Type: BI Var: 1
L.O.: 4.2.2
69) Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. Use the p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.1;4.3.2
Use the following to answer the questions below:
A Division III college men's basketball team is interested in identifying factors that impact the outcomes of their games. They plan to use "point spread" (their score minus their opponent's score) to quantify the outcome of each game this season; positive values indicate games that they won while negative values indicate games they lost. They want to determine if "steal differential" (the number of steals they have in the game minus the number of steals their opponent had) is related to point spread; positive values indicate games where they had more steals than their opponent. The data for the games they played this season displayed in the provided table.
Point Spread (y) | Steal Differential (x) | Point Spread (y) | Steal Differential (x) |
4 | 7 | 18 | -2 |
2 | -2 | 2 | 5 |
-21 | -2 | -6 | -6 |
-4 | 1 | 7 | 4 |
-9 | 2 | 13 | -1 |
7 | -5 | 3 | -3 |
-7 | 1 | 3 | 1 |
15 | -2 | 10 | -2 |
7 | -1 | 20 | 0 |
-13 | -2 | -1 | 1 |
-11 | -6 | -1 | -3 |
-17 | -3 | -11 | -2 |
31 | 7 |
Assuming that this season was a typical season for the team, they want to know if steal differential is positively correlated with point spread.
70) Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.2
71) Use technology to determine if this sample provides evidence that point spread and steal differential are positively correlated. Be sure to include all of the steps of the test. Use a 10% significance level to make your conclusion.
Hypotheses: : ρ = 0 versus : ρ > 0
The p-value is about 0.038. (Answers may vary.)
Because the p-value is less than the significance level, we would reject the null hypothesis and we have evidence that point spread and steal differential are positively correlated.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.3.1; 4.3.2; 4.4.3; 4.4.4
Use the following to answer the questions below:
A Division III college men's basketball team is interested in identifying factors that impact the outcomes of their games. They plan to use "point spread" (their score minus their opponent's score) to quantify the outcome of each game this season; positive values indicate games that they won while negative values indicate games they lost. They want to determine if "steal differential" (the number of steals they have in the game minus the number of steals their opponent had) is related to point spread; positive values indicate games where they had more steals than their opponent. The data for the games they played this season displayed in the provided table.
Point Spread (y) | Steal Differential (x) | Point Spread (y) | Steal Differential (x) |
4 | 7 | 18 | -2 |
2 | -2 | 2 | 5 |
-21 | -2 | -6 | -6 |
-4 | 1 | 7 | 4 |
-9 | 2 | 13 | -1 |
7 | -5 | 3 | -3 |
-7 | 1 | 3 | 1 |
15 | -2 | 10 | -2 |
7 | -1 | 20 | 0 |
-13 | -2 | -1 | 1 |
-11 | -6 | -1 | -3 |
-17 | -3 | -11 | -2 |
31 | 7 |
Assuming that this season was a typical season for the team, they want to know if steal differential is positively correlated with point spread.
72) Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that steal differential is positively correlated with point spread.
A) Parameter: ρ = correlation between point spread and steal differential for this team.
Hypotheses: : ρ = 0 versus : ρ > 0
B) Parameter: ρ = correlation between point spread and steal differential for this team.
Hypotheses: : ρ = 0 versus : ρ < 0
C) Parameter: ρ = correlation between point spread and steal differential for this team.
Hypotheses: : ρ = 0 versus : ρ ≠ 0
D) Parameter: ρ = correlation between point spread and steal differential for this team.
Hypotheses: : ρ ≠ 0 versus : ρ = 0
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
73) Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.2
74) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.3
75) Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.1;4.3.5
4.5 Making Connections
1) An article published in the Canadian Journal of Zoology presented a method for estimating the body fat percentage of North American porcupines; the method was illustrated with a sample of porcupines. Based on this sample, a 95% bootstrap confidence interval for the average body fat percentage of porcupines is 17.4% to 25.8%. Which of the following null hypotheses would be rejected based on this confidence interval?
A) : μ = 19.1%
B) : μ = 31.0%
C) : μ = 20.6%
D) : μ = 24.7%
Diff: 2 Type: BI Var: 1
L.O.: 4.5.1
2) Suppose that a 95% confidence interval for μ is (54.8, 60.8). Which of the following is most likely the p-value for the test of versus
A) 0.031
B) 0.001
C) 0.016
D) 0.231
Diff: 3 Type: BI Var: 1
L.O.: 4.5.2
3) Briefly explain the difference between a "bootstrap distribution" and a "randomization distribution".
A randomization distribution is used in hypothesis testing and is created by forcing the sample to be consistent with the null hypothesis before repeatedly resampling. This generates a distribution of sample outcomes that are reasonable under the null hypothesis. This distribution is then used to estimate a p-value by comparing a statistic from the original sample to the randomization distribution.
Diff: 3 Type: ES Var: 1
L.O.: 4.5.0
Use the following to answer the questions below:
A study conducted by the National Center of Health Statistics collects data on Vitamin D levels. In 2011-2014, in a sample of 3,929 non-Hispanic Blacks showed that 17.5% were Vitamin D deficient. A 95% confidence interval based on the sample is (0.152, 0.200).
4) Define the appropriate parameter and state the appropriate hypotheses for testing the claim that, among African Americans, Vitamin D deficiency occurs at a rate other than 8%.
A) Parameter: p = proportion of non-Hispanic Blacks that are Vitamin D deficient
Hypotheses: versus
B) Parameter: p = proportion of non-Hispanic Blacks that are Vitamin D deficient
Hypotheses: versus
C) Parameter: p = proportion of non-Hispanic Blacks that are Vitamin D deficient
Hypotheses: versus
D) Parameter: p = proportion of non-Hispanic Blacks that are Vitamin D deficient
Hypotheses: versus
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
5) Does this confidence interval provide evidence that among non-Hispanic Blacks Vitamin D deficiency occurs at a rate other than 8%? What significance level is being used to make this decision? Briefly justify your answer.
Diff: 2 Type: ES Var: 1
L.O.: 4.5.2
6) In a test of the hypotheses : = versus : ≠ , the observed sample results in a p-value of 0.0256. Would you expect a 95% confidence interval for based on this sample to contain 0?
A) Yes
B) No
Diff: 3 Type: MC Var: 1
L.O.: 4.5.1
7) In January 2015 Gallup reported the results from a survey of 167,000 U.S. adults from January - June 2014 for the Gallup-Healthways Well-Being Index. Based on self-reported height and weight data, they found that 62.8% of U.S. adults are overweight or obese. A 95% confidence interval for the proportion of U.S. adults that are overweight or obese is (0.626, 0.63). Does this interval support the claim that "two-thirds of Americans are overweight or obese"?
A) Yes
B) No
Diff: 2 Type: MC Var: 1
L.O.: 4.5.2
Use the following to answer the questions below:
The makers of a popular brand of laundry detergent have discovered a new secret ingredient that they believe will boost the cleaning power of their detergent. The new ingredient is expensive, and if they use it, they would have to increase the retail price of the detergent (and they worry that the price increase will cause them to lose customers). However, they believe that if the improved detergent gets clothes drastically cleaner, customers will recognize that it is worth the extra cost. They conduct an experiment to compare the performance of the new and old formulas at removing grass stains, red wine, and chocolate from white t-shirts. Each cleaned shirt was rated on a scale from 1 (stain did not get removed) to 10 (no evidence of the stain) by trained experts. They compared the average rating for the new and old formulas.
8) Briefly explain what a Type II error would mean in this situation.
Diff: 2 Type: ES Var: 1
L.O.: 4.3.3
9) Suppose they find that the average rating for the shirts cleaned with the new formula was 8.2 and the average rating for the shirts cleaned with the old formula is 8.0 Do you think these results are practically significant? Briefly explain.
Probably not. The difference in the averages is fairly small. Even if the new formula does get clothes cleaner, it is likely that is not a "drastic" improvement (and it is entirely possible that a customer couldn't tell the difference). If there is a risk of losing customers because of a price increase, it is likely not worth it (and thus not practically significant) since the new formula provides only a small improvement.
Diff: 2 Type: ES Var: 1
L.O.: 4.5.3
10) Suppose, at the 5% significance level, they find that the new formula cleaned the shirts significantly better than the old formula, with a p-value of 0.046. Interpret the p-value, in terms of the probability of the results happening by random chance, in this context.
Diff: 2 Type: ES Var: 1
L.O.: 4.2.1
Use the following to answer the questions below:
In May 2012, President Obama made history by revealing his support of gay marriage. Around that time, the Gallup Organization polled 1,024 U.S. adults about their opinions on gay/lesbian relations and gay marriage. They found that 54% of those sampled viewed gay/lesbian relations as "morally acceptable" and that 50% felt that gay marriage should be legal.
11) Does this sample provide evidence that the majority of Americans find gay/lesbian relations "morally acceptable"? Describe how you could generate a single randomization sample in this situation, and identify the statistic that you would calculate for each sample.
Diff: 2 Type: ES Var: 1
L.O.: 4.4.1
12) Use technology to determine if this sample provides evidence that the majority of Americans find gay/lesbian relations "morally acceptable". Be sure to state the hypotheses, give the p-value, and clearly state the conclusion in context. Include an assessment of the strength of the evidence.
Hypotheses: : p = 0.50 versus : p > 0.50
The observed sample statistic is = 0.54. The p-value is the proportion of the dots that are greater than or equal to 0.54. Actual answers will vary, but the p-value should be near 0.005.
This p-value provides very strong evidence that the majority of Americans find gay/lesbian relations to be "morally acceptable."
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.3; 4.4.4
13) Use the provided randomization distribution (based on 1,000 samples) to determine if this sample provides evidence that the majority of Americans find gay/lesbian relations "morally acceptable". Be sure to state the hypotheses, give the p-value, and clearly state the conclusion in context. Include an assessment of the strength of the evidence.
Parameter: p = proportion of Americans who find gay/lesbian relations "morally acceptable"
Hypotheses: : p = 0.50 versus : p > 0.50
The observed sample statistic is = 0.54. The p-value is the proportion of the 1,000 dots that are greater than or equal to 0.54 (5 or 7 should be accepted), thus either 0.005 or 0.007 should be accepted as the p-value for this test.
This p-value provides very strong evidence that the majority of Americans find gay/lesbian relations to be "morally acceptable."
Note that this conclusion is based on the interpretation of the p-value as the strength of the evidence against the null hypothesis, but the same conclusion would be reached at any reasonable significance level.
Diff: 2 Type: ES Var: 1
L.O.: 4.1.2; 4.2.2; 4.2.5; 4.3.2; 4.3.5; 4.4.4
14) Define the appropriate parameter and state the hypotheses for testing if this sample provides evidence that the proportion of American adults who support gay marriage differs from 50%.
A) Parameter: p = proportion of American adults who support gay marriage
Hypotheses: : p = 0.50 versus : p ≠ 0.50
B) Parameter: p = proportion of American adults who support gay marriage
Hypotheses: : p ≠ 0.50 versus : p = 0.50
C) Parameter: p = proportion of American adults who support gay marriage
Hypotheses: : p = 0.50 versus : p > 0.50
D) Parameter: p = proportion of American adults who support gay marriage
Hypotheses: : p = 0.50 versus : p < 0.50
Diff: 2 Type: BI Var: 1
L.O.: 4.1.2
15) A 90% confidence interval for the proportion of American adults who support gay marriage is (0.475, 0.524). Does this confidence interval provide evidence that the percentage of American adults who support gay marriage differs from 50%? State the significance level you are using.
A) No; significance level of 10%
B) No; significance level of 5%
C) Yes; significance level of 10%
D) Yes; significance level of 5%
Diff: 2 Type: BI Var: 1
L.O.: 4.5.2
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