Ch.9 Comparing More Than Two Means Test Questions & Answers

Chapter 9

Introduction to Statistical Investigations Test Bank

Note: TE = Text entry TE-N = Text entry - Numeric

Ma = Matching MS = Multiple select

MC = Multiple choice TF = True-False

DD = Drop-down

CHAPTER 9 LEARNING OBJECTIVES

9.1: Carry out a simulation-based analysis for comparing multiple population means using a Mean Group Diff statistic.

9.2: Carry out a theory-based analysis for comparing multiple population means using an F-statistic.

9.1-1: Understand how multiple comparisons can increase the probability of a Type I error.

9.1-2: Apply the Mean Group Diff statistic to a dataset, including the relationship with the statistic comparing two means.

9.1-3: Understand that larger values of the Mean Group Diff statistic suggest stronger evidence against the null hypothesis.

9.1-4: Use the 3S strategy with the Mean Group Diff statistic.

9.1-5: Use the Multiple Means applet to carry out an analysis using the Mean Group Diff statistic to compare multiple means.

9.1-6: Understand why the simulated null distribution of the Mean Group Diff statistic looks different from other simulated null distributions.

9.1-7: Conduct a follow-up test after using the Mean Group Diff statistic.

Questions 1 through 6: In a neurological study of the effect of environment on mental development, rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage – housed alone), Standard (cage with other rats), Enriched (cage with other rats and toys), and Super Enriched (cage with other rats and toys changed on a periodic basis). After two months, the rats were tested on a variety of learning measures, one of them being the number of attempts needed to learn to navigate a maze. The data for the maze task are below, along with means and standard deviation for each group.

1. What are the observational units?
   1. Months
   2. Toys
   3. Test conditions
   4. Rats
2. Which of the following plots would be appropriate to investigate the relationship between test condition and number of attempts needed to learn to navigate a maze? Select all that apply.
   1. Scatterplot
   2. Segmented bar graph
   3. Side-by-side boxplots
   4. Stacked dot plots
3. What is the value of the Mean Group Diff statistic?

LO: 9.1-2; Difficulty: Medium; Type: TE-N

1. A simulated null distribution of 1,000 Mean Group Diff statistics follows.

Describe how to use this distribution to calculate the p-value.

• 1. Count the proportion of samples less than or equal to 5.967.
  2. Count the proportion of samples greater than or equal to 5.967.
  3. Count the proportion of samples greater than or equal to 14.45.
  4. Count the proportion of samples less than or equal to -5.967 and greater than or equal to 5.967.

1. Does the analysis using the Mean Group Diff statistic allow you to determine which test conditions differ significantly from which others?
   1. Yes, since the Mean Group Diff statistic was statistically significant.
   2. Yes, since the sample means across groups differ.
   3. No, since it is an overall test.
   4. No, since the sample size is too small.
2. Suppose that, in reality, there is no association between test condition and number of attempts needed to learn to navigate a maze. Which of the following sets of tests would have the largest probability of at least one Type I error?
   1. and
   2. and
   3. 
   4. 
   5. and and
3. True or False: As the Mean Group Diff statistic increases, the p-value also increases.
4. True or False: A simulated null distribution of the Mean Group Diff statistic will always be symmetric.
5. True or False: The Mean Group Diff statistic cannot be negative.
6. The two graphs, A and B, show dotplots from two different data sets. Suppose I want to compare the means in A and do another comparison of means in B. For each case I compute a MAD statistic. Which of the following will be true about these statistics?

• 1. The MAD statistic is the same in A and B.
  2. The MAD statistic is larger in A than in B.
  3. The MAD statistic is smaller in A than in B.
  4. We cannot tell if the MAD statistic will be larger in A or B.

Questions 11 through 15: College students tested to see if how well you know a person affects your ability to detect a lie from that person.  To do this, they came up with 10 statements about a person in their group. Five of these statements were true and five were False. The group tried to make up statements that nobody (not even close friends) would know if they were true or False. The students then presented these statements to people that fit in three groups: close friends, acquaintances, and complete strangers and counted how many statements each person correctly identified as true or False. A summary of the results are as follows.

State the null and alternative hypotheses.

• 1. versus
  2. versus
  3. versus
  4. versus

1. Compute the Mean Group Diff statistic for this data set.

LO: 9.1-2; Difficulty: Medium; Type: TE-N

1. A null distribution was generated for this example and is shown. What is the shape of this distribution?
   1. Normal
   2. Symmetric
   3. Left skewed
   4. Right skewed
2. Using the simulated null distribution of Mean Group Diff statistics in question 13, what is the strength of evidence against the null hypothesis?
   1. Strong evidence against the null
   2. Moderate evidence against the null
   3. Weak evidence against the null
   4. No evidence against the null
3. If the Mean Group Diff statistic had been smaller than the observed Mean Group Diff statistic calculated in question 12, how would the strength of evidence change?
   1. The strength of evidence against the null would increase.
   2. The strength of evidence against the null would decrease.
   3. The strength of evidence against the null would stay the same.

9.2-1: Find the value of the ANOVA F-statistic using the Multiple Means applet, recognize that larger values of the statistic indicate more evidence against the null hypothesis and why the distribution of the F-statistic is skewed right.

9.2-2: Identify whether an ANOVA (F) test meets appropriate validity conditions.

9.2-3: Conduct an ANOVA using the Multiple Means applet, including appropriate follow-up tests.

1. The two graphs, A and B, show dotplots from two different data sets. Suppose I want to compare the means in A and do another comparison of means in B. For each case I compute an F-statistic. Which of the following will be true about these statistics?

• 1. The F-statistic is the same in A and B.
  2. The F-statistic is larger in A than in B.
  3. The F-statistic is smaller in A than in B.
  4. We cannot tell if the F-statistic will be larger in A or B.

1. When performing an ANOVA F-test, which definition of a p-value is the most accurate?
   1. The p-value is the probability that the observed F-statistic will occur again.
   2. If the null hypothesis is true, the p-value is the probability of observing an F-statistic as large or larger than the one actually observed.
   3. The p-value is the value that an F-statistic must reach in order to be significant under the null hypothesis.
   4. The p-value is the probability that the null hypothesis is true.
2. Why do you do overall tests when comparing multiple means and not just do the follow-up confidence intervals?
   1. Doing an overall test will more likely lead to significant results than just doing the follow-up confidence intervals.
   2. Doing an overall test allows us to see exactly which group is significantly different from which other groups.
   3. Doing an overall test allows us to quickly get our results, while the follow-up confidence intervals are very time-consuming.
   4. Doing an overall test allows us to keep the probability of a type I error at 5% or whatever significance level we would like.
3. True or False: As the F statistic increases, the p-value decreases.
4. True or False: The F statistic can be negative.
5. True or False: The F-statistic is the ratio of the variability between the groups over the variability within the groups.

Questions 22 and 23: An experiment is conducted which randomly places students into one of three treatment groups: (1) those students who will take a test that is printed on white paper, (2) those who will take the same test, but printed on red paper, and (3) those who will take the same test, but printed on blue paper. The researcher analyzes the data using ANOVA in order to compare the average scores in the three groups looking for evidence that the average score is different on at least one of the three tests. Assume that there really is a difference (at least one group is different) when answering questions 22 and 23.

1. As the size of the sample in each group increases, all else remaining the same, what will be the impact on the strength of evidence for finding a difference in the average scores on the three exams?
   1. There will be more evidence of a difference.
   2. There will be less evidence of a difference.
   3. There will be no impact on the strength of evidence of a difference.
   4. There is not enough information to tell.
2. If changing the third treatment group from blue to purple increases the difference in the purple group’s average score from the other two groups, all else remaining the same, what will be the impact on the strength of evidence for finding a difference in the average scores on the three exams?
   1. There will be more evidence of a difference.
   2. There will be less evidence of a difference.
   3. There will be no an impact on the strength of evidence of a difference.
   4. There is not enough information to tell.

Questions 24 through 30: A British study examined whether the type of background music playing in a restaurant affected the amount of money that diners spent on their meals.  The researchers asked a restaurant to alternate silence, popular music, and classical music on successive nights over eighteen days.  Each type of music was played for 6 nights (the order was randomly determined to guard against confounding). The type of music played and the amount spent on food and drinks (in British pounds) for each of 393 customers was recorded. The data are summarized below.

1. What is the null hypothesis? Select all that apply.
   1. The long-run average amount spent on a meal while listening to music is the same for all three conditions – classical, pop, or none.
   2. The sample average amount spent on a meal while listening to music is the same for all three conditions – classical, pop, or none.
   3. 
   4. 
2. Which of the following validity conditions are met to conduct an ANOVA F-test on these data? Select all that apply.
   1. The standard deviations of the sample are approximately equal.
   2. The sample sizes are all at least 20.
   3. The sample distributions show no strong skewness.
   4. The sample means are all at least 20.
3. Compute the F-statistic using the summary statistics listed.

MSTreatment =

MSError =

F = MSTreatment/MSError = 27.24

1. The p-value for the ANOVA F-test is less than 0.001. How would you interpret this value?
   1. In less than 0.1% of all samples, the F-statistic would be as large or larger than the one observed, assuming there is no association between music type and amount spent on food and drinks.
   2. In less than 0.1% of all samples, the F-statistic would be as small or smaller than the one observed, assuming there is no association between music type and amount spent on food and drinks.
   3. In less than 0.1% of all samples, the F-statistic would be as large or larger than the one observed, assuming there is an association between music type and amount spent on food and drinks.
   4. In less than 0.1% of all samples, the F-statistic would be as small or smaller than the one observed, assuming there is an association between music type and amount spent on food and drinks.
2. Follow-up 95% confidence intervals are presented below.

True or False: The mean amount spent when classical music is playing is significantly higher than the mean amount spent when no music is playing.

1. Follow-up 95% confidence intervals are presented below.

True or False: The mean amount spent when pop music is playing is significantly higher than the mean amount spent when no music is playing.

1. Follow-up 95% confidence intervals are presented below.

True or False: The mean amount spent when pop music is playing is significantly lower than the mean amount spent when classical music is playing.