Test Bank Chapter 2 Describing Data

Statistics - Unlocking the Power of Data, 3e (Lock)

Chapter 2 Describing Data

2.1 Categorical Variables

Use the following to answer the questions below:

February 12, 2009 marked the anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 Americans about their education level and their beliefs about the theory of evolution. The survey results are displayed in the provided two-way table.

1) What proportion of respondents have a college degree? Round your answer to three decimal places.

Diff: 1 Type: SA Var: 1

L.O.: 2.1.4

2) What proportion of respondents have no opinion on the theory of evolution? Round your answer to two decimal places.

Diff: 1 Type: SA Var: 1

L.O.: 2.1.4

3) What proportion of non-believers have a high school education or less? Use four decimal places in your answer.

Diff: 2 Type: SA Var: 1

L.O.: 2.1.4

4) What proportion of college graduates believe in the theory of evolution? Use four decimal places in your answer.

Diff: 2 Type: SA Var: 1

L.O.: 2.1.4

5) Find the proportion of respondents who believe in evolution for each education level (round each to three decimal places). Does there seem to be an association between education level and belief in evolution? If so, in what direction?

HS or less: 0.211

Some College: 0.409

College Graduate: 0.531

Postgraduate: 0.741

There does seem to be an association between education level and belief in evolution. Individuals with more education are more likely to believe in evolution.

Diff: 3 Type: ES Var: 1

L.O.: 2.1.4

6) The survey results are displayed in the segmented bar chart. Does there appear to be an association between education level and belief in the theory of evolution? If so, what does it mean about these two variables?

Students might also notice that there are more respondents with a high school education or less, and that the number of respondents in each education category decreases as education level increases, however, these observations, though useful and informative, are not about the relationship between the two variables.

Diff: 3 Type: ES Var: 1

L.O.: 2.1.5

Use the statement to answer the following questions below.

7) A Fun-Size bag of M&M's contains 4 green, 4 red, 3 yellow, 4 orange, 4 blue, and 3 brown candies.

What proportion of the M&M's are green? Use four decimal places in your answer.

Diff: 1 Type: SA Var: 1

L.O.: 2.1.2

8) A Fun-Size bag of M&M's contains 5 green, 4 red, 4 yellow, 3 orange, 4 blue, and 4 brown candies.

What proportion of the candies are yellow or orange? Use four decimal places in your answer.

Diff: 1 Type: SA Var: 1

L.O.: 2.1.2

9) A Fun-Size bag of M&M's contains 5 green, 3 red, 3 yellow, 3 orange, 4 blue, and 3 brown candies.

Sketch a bar chart of the data.

Diff: 1 Type: ES Var: 1

L.O.: 2.1.1

10) A Fun-Size bag of M&M's contains 4 green, 2 red, 4 yellow, 3 orange, 6 blue, and 1 brown candies.

Construct a relative frequency table of the results. Use two decimal places in your relative frequencies.

Diff: 1 Type: ES Var: 1

L.O.: 2.1.1

Use the following to answer the questions below:

In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked, "In general, how much trust and confidence do you have in the mass media—such as newspapers, TV, and radio—when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all."

11) Display the results in a frequency table.

Diff: 1 Type: ES Var: 1

L.O.: 2.1.1

12) Sketch a bar chart of the data.

Diff: 1 Type: ES Var: 1

L.O.: 2.1.1

13) Give a relative frequency table of the data. Use two decimal places in your relative frequencies.

Diff: 1 Type: ES Var: 1

L.O.: 2.1.1

14) What proportion of respondents have a great deal of confidence in the media? Use two decimal places in your answer.

Diff: 1 Type: SA Var: 1

L.O.: 2.1.2

15) What proportion of respondents have a negative opinion (not very much confidence/none at all) about the mass media? Use two decimal places in your answer.

Diff: 2 Type: SA Var: 1

L.O.: 2.1.2

16) In the article, they discuss the association between political party and opinion about the media ("positive" = great deal/fair amount of confidence and "negative" = not very much confidence/none at all). The results, as percentages, are displayed in the side-by-side bar charts. Describe the association between political party and opinion about the media. Use the bar chart to estimate the proportion of individuals with positive opinions about the media for each political party.

Diff: 2 Type: ES Var: 1

L.O.: 2.1.5

17) In the same article, they compare opinions about the media in 2012 to those in the previous election year (2008). In 2008, 60% of Democrats, 27% of Republicans, and 41% of Independents had positive opinions (great deal/fair amount of confidence) about the media. For each political party, find the difference in the proportion of positive opinions in 2008 and the proportion of positive opinions in 2012. Comment on if/how opinions have changed for the political parties over the past four years.

Democrats: - = 0.60 - 0.58 = 0.02

Independents: - = 0.41 - 0.31 = 0.10

The proportion of people with positive views on the media have decreased over the last four years for all parties. The Democrats and Republicans saw only small changes in this proportion, 0.02 and 0.01 respectively. The Independents had the largest change in the proportion of people with positive views on the media, with a decrease of 10% (0.10).

Diff: 2 Type: ES Var: 1

L.O.: 2.1.1

Use the following to answer the questions below:

In a recent survey, Gallup asked a sample of U.S. adults if they would prefer to have a job outside the home, or if they would prefer to stay home to care for the family and home. Partial results for the individuals who expressed a preference, broken down by gender, are displayed in the two-way table.

18) Find the number of males who would prefer to stay at home.

Diff: 2 Type: SA Var: 1

L.O.: 2.1.3

19) What proportion of respondents would prefer to stay at home? Round your answer to two decimal places.

Diff: 1 Type: SA Var: 1

L.O.: 2.1.4

20) Compute the difference in the proportion of men who would prefer a job outside of the home and the proportion of females who would prefer a job outside of the home. Use two decimal places in your answer.

Diff: 1 Type: SA Var: 1

L.O.: 2.1.4

21) Students in a small statistics class were asked which was their dominant hand and if they were in a STEM (science, technology, engineering, and math) major. Their results are listed below. Use the results to construct a two-way table.

Diff: 2 Type: ES Var: 1

L.O.: 2.1.3

2.2 One Quantitative Variable: Shape and Center

1) If a distribution is heavily skewed to the left, which relationship between the mean and median is most likely?

A) Mean < Median

B) Mean ≈ Median

C) Mean > Median

Diff: 2 Type: MC Var: 1

L.O.: 2.2.4

2) If a distribution is roughly symmetric, which relationship between the mean and median is likely true?

A) Mean < Median

B) Mean ≈ Median

C) Mean > Median

Diff: 2 Type: MC Var: 1

L.O.: 2.2.4

3) If a distribution is heavily skewed to the right, which relationship between the mean and median is likely true?

A) Mean < Median

B) Mean ≈ Median

C) Mean > Median

Diff: 2 Type: MC Var: 1

L.O.: 2.2.4

Use the dataset to calculate the following summary statistics in the questions below. Report each with one decimal place.

4)

Median

Diff: 1 Type: SA Var: 1

L.O.: 2.2.2

5)

Mean

Diff: 1 Type: SA Var: 1

L.O.: 2.2.2

Use the following to answer the questions below:

The provided histogram displays the number of Facebook friends for students in a small statistics class.

6) Which of the following best describes the shape of the distribution of the number of Facebook friends?

A) Skewed to the left

B) Roughly symmetric

C) Skewed to the right

Diff: 1 Type: MC Var: 1

L.O.: 2.2.1

7) The mean number of Facebook friends is closest to which value?

A) 220 friends

B) 560 friends

C) 810 friends

D) 1,000 friends

Diff: 2 Type: MC Var: 1

L.O.: 2.2.3

8) The median number of Facebook friends is likely closest to which value?

A) 300

B) 500

C) 700

D) 800

Diff: 2 Type: MC Var: 1

L.O.: 2.2.3

Use the following to answer the questions below:

The finishing time for the top 100 men in a marathon are displayed in the provided figure.

9) Which of the following best describes the distribution of times for the top 100 male finishers in the marathon?

A) Skewed to the left

B) Roughly symmetric

C) Skewed to the right

Diff: 1 Type: MC Var: 1

L.O.: 2.2.1

10) The mean time for the top 100 males is closest to which value?

A) 148 minutes

B) 151 minutes

C) 140 minutes

D) 135 minutes

Diff: 2 Type: MC Var: 1

L.O.: 2.2.3

11) The median time for the top 100 males is closest to which value?

A) 156 minutes

B) 140 minutes

C) 145 minutes

D) 151 minutes

Diff: 2 Type: MC Var: 1

L.O.: 2.2.3

Use the following to answer the questions below:

The midrange is another way to measure of the center of a distribution. The midrange of a dataset is defined to be the average of the minimum and maximum values in the dataset.

12) Calculate the midrange of this dataset.

Diff: 2 Type: SA Var: 1

L.O.: 2.2.0

13) In general, would you think that the midrange should be a resistant statistic?

A) Yes

B) No

Diff: 3 Type: MC Var: 1

L.O.: 2.2.4

2.3 One Quantitative Variable: Measures of Spread

1) Which statistic is more resistant to outliers (or extreme data values)?

A) Mean

B) Median

Diff: 2 Type: BI Var: 1

L.O.: 2.2.4;2.3.6

2) Which statistic is more resistant to outliers (or extreme data values)?

A) Interquartile Range

B) Standard Deviation

Diff: 2 Type: BI Var: 1

L.O.: 2.3.6

Use the dataset to compute the following summary statistics in the questions below.

3)

Median

Diff: 1 Type: SA Var: 1

L.O.: 2.2.2

4)

Mean (rounded to two decimal places)

Diff: 1 Type: SA Var: 1

L.O.: 2.2.2

5)

Q1

Diff: 1 Type: SA Var: 1

L.O.: 2.3.1

6)

Q3

Diff: 1 Type: SA Var: 1

L.O.: 2.3.1

7)

IQR

Diff: 1 Type: SA Var: 1

L.O.: 2.3.5

8)

Range

Diff: 1 Type: SA Var: 1

L.O.: 2.3.5

9) Each of the variables displayed in the histograms below has a mean of 14.5, a range of 8, and 59 observations. Rank the three variables according to their standard deviations, from the smallest to the largest.

A) A, B, C

B) B, A, C

C) C, B, A

D) A, C, B

Diff: 3 Type: BI Var: 1

L.O.: 2.3.2

Use the following statement to answer the questions below.

10) The distribution of waiting times at the student health center is bell-shaped with a mean of 13 minutes and a standard deviation of 2. Give an interval that is likely to contain about 95% of wait times.

A) 9 to 17 minutes

B) 11 to 15 minutes

C) 7 to 19 minutes

D) 9 to 13 minutes

Diff: 2 Type: BI Var: 1

L.O.: 2.3.2

11) The distribution of waiting times at the student health center is bell-shaped with a mean of 10 minutes and a standard deviation of 3. Find the z-score of someone who waits 5 minutes. Round your z-score to two decimal places. Be sure to specifically indicate if a wait time of 5 minutes is unusual.

A) -1.67; The wait time is not unusual.

B) 1.67; The wait time is unusual.

C) -1.67; The wait time is unusual.

D) 1.67; The wait time is not unusual.

Diff: 2 Type: BI Var: 1

L.O.: 2.3.3

Use the following to answer the questions below:

Scores on an exam (out of 100 points) given in a large introductory statistics course are displayed in the provided histogram.

12) Which best describes the shape of the distribution of exam scores?

A) Approximately symmetric

B) Skewed to the left

C) Skewed to the right

Diff: 1 Type: BI Var: 1

L.O.: 2.2.1

13) Based on the histogram, which value is likely the mean exam score?

A) 82

B) 88

C) 76

D) 92

Diff: 1 Type: BI Var: 1

L.O.: 2.2.3

14) Based on the histogram of exam scores, which value is likely the median exam score?

A) 92

B) 88

C) 82

D) 72

Diff: 1 Type: BI Var: 1

L.O.: 2.2.3

15) Based on the histogram, the standard deviation of the exam scores is likely closest to which of these values?

A) 0.5

B) 10

C) 5

D) 1

Diff: 3 Type: BI Var: 1

L.O.: 2.3.2;2.3.5

2.4 Boxplots and Quantitative/Categorical Relationships

Use the following to answer the questions below:

One of the symptoms of the flu is an elevated pulse rate. Pulse rates (in beats per minute) for patients with the flu are provided.

1) Give the sample mean pulse rate. Use two decimal places in your answer.

A) 89.35 beats per minute

B) 90 beats per minute

C) 92.5 beats per minute

D) 89 beats per minute

Diff: 1 Type: BI Var: 1

L.O.: 2.2.2

2) Find the standard deviation of the pulse rates. Use two decimal places in your answer.

A) 7.85 beats per minute

B) 8.27 beats per minute

C) 7.33 beats per minute

D) 8.19 beats per minute

Diff: 2 Type: BI Var: 1

L.O.: 2.3.1

3) Give the five-number summary of these pulse rates.

bpm = beats per minute

Summaries from Minitab:

bpm = beats per minute

Diff: 1 Type: ES Var: 1

L.O.: 2.3.1;2.3.4

4) Are there any outliers? If so, which data points? Clearly show your work to justify your answer.

Using Q1 and Q3 found in R:

Use the 1.5 IQR rule to detect outliers.

IQR = 93 - 83.50 = 9.5

1.5 IQR = 14.25

An observation is an outlier if it is smaller than

83.5 - 14.25 = 69.25 bpm

or larger than

93 + 14.25 = 107.25 bpm.

There is only one outlier, 110 bpm.

Diff: 2 Type: ES Var: 1

L.O.: 2.4.1

Use the following to answer the questions below:

Match the five-number summary to the appropriate boxplot.

5) ________ 15, 19, 20, 25, 28

Diff: 1 Type: SA Var: 1

L.O.: 2.3.4;2.4.2

6) ________ 1, 3, 4, 6, 8

Diff: 1 Type: SA Var: 1

L.O.: 2.3.4;2.4.2

7) ________ 3, 10, 12, 13, 19

Diff: 1 Type: SA Var: 1

L.O.: 2.3.4;2.4.2

8) ________ 5, 8, 9, 11, 14

Diff: 1 Type: SA Var: 1

L.O.: 2.3.4;2.4.2

Use the following to answer the questions below:

The provided Minitab output displays descriptive statistics for the amount of financial aid, in thousands of dollars, awarded to a sample of students at a large university.

9) How many students are included in the sample?

Diff: 1 Type: SA Var: 1

L.O.: 2.3.1

10) Based on the mean and median financial aid amounts displayed in the summary, which of the following most likely describes the shape of the distribution of financial aid amounts?

A) Slightly skewed to the left

B) Roughly symmetric

C) Slightly skewed to the right

Diff: 2 Type: BI Var: 1

L.O.: 2.2.4

11) Based on the output, give an interval that is certain to contain the 15th percentile of the distribution of financial aid amounts.

Diff: 3 Type: ES Var: 1

L.O.: 2.3.4

12) Based on the output, give an interval that is certain to contain the 60th percentile of the distribution of financial aid amounts.

Diff: 3 Type: ES Var: 1

L.O.: 2.3.4

13) What is the range of financial aid amounts?

Diff: 1 Type: SA Var: 1

L.O.: 2.3.5

14) What is the IQR of financial aid amounts?

Diff: 2 Type: SA Var: 1

L.O.: 2.3.5

15) Is the largest financial aid amount an outlier?

A) Yes

B) No

Diff: 2 Type: MC Var: 1

L.O.: 2.4.1

16) Find and interpret the z-score for the smallest financial aid amount.

Diff: 2 Type: SA Var: 1

L.O.: 2.3.3

Use the following to answer the questions below:

Students in an introductory statistics course were asked to count the number of scars on their dominant hand (the one they write with the most). The results are displayed in the provided boxplot.

17) From the boxplot you can identify how many students are in the class.

Diff: 2 Type: TF Var: 1

L.O.: 2.4.2

18) Use the boxplot to estimate the median number of scars that students in the class have on their dominant hand.

Diff: 2 Type: SA Var: 1

L.O.: 2.4.2

19) The distribution of the number of scars would be classified as

A) skewed to the left.

B) roughly symmetric.

C) skewed to the right.

Diff: 2 Type: BI Var: 1

L.O.: 2.4.2

20) Calculate the IQR for the distribution of the number of scars students have.

Diff: 2 Type: SA Var: 1

L.O.: 2.3.5;2.4.2

21) Which answer best describes the following conclusion?

"There are no students with 7 scars on their dominant hand."

A) True

B) False

C) Cannot be determined

Diff: 3 Type: MC Var: 1

L.O.: 2.4.2

22) Which answer best describes the following conclusion?

"There are no students with 2 scars on their dominant hand."

A) True

B) False

C) Cannot be determined

Diff: 3 Type: MC Var: 1

L.O.: 2.4.2

23) The mean can be determined exactly from the boxplot.

Diff: 2 Type: TF Var: 1

L.O.: 2.4.2

Use the following to answer the questions below:

The side-by-side boxplots compare the top 100 men's and women's finishing times in a marathon.

24) Which group tends to finish the race faster?

A) Men

B) Women

Diff: 2 Type: BI Var: 1

L.O.: 2.4.4

25) Which group has the larger spread in its race times?

A) Men

B) Women

Diff: 2 Type: BI Var: 1

L.O.: 2.4.4

26) Does there appear to be an association between gender and race time?

A) Yes

B) No

Diff: 2 Type: MC Var: 1

L.O.: 2.4.4

Use the following to answer the questions below:

The states located in the Midwestern region of the country typically experience a large number of tornados every year. The number of tornadoes from 2000-2011 for four Midwestern states (Kansas, Nebraska, South Dakota, and Iowa) are displayed in the side-by-side boxplots.

27) Which state tends to see the most tornadoes per year?

A) Kansas

B) Nebraska

C) South Dakota

D) Iowa

Diff: 1 Type: BI Var: 1

L.O.: 2.4.3

28) Which state has the largest range?

A) Kansas

B) Nebraska

C) South Dakota

D) Iowa

Diff: 2 Type: BI Var: 1

L.O.: 2.43

29) Which state tends to see the fewest tornadoes per year?

A) Kansas

B) Nebraska

C) South Dakota

D) Iowa

Diff: 1 Type: BI Var: 1

L.O.: 2.4.3

30) Which state has the largest IQR?

A) Kansas

B) Nebraska

C) South Dakota

D) Iowa

Diff: 2 Type: BI Var: 1

L.O.: 2.4.3

31) Which state has an outlier?

A) Kansas

B) Nebraska

C) South Dakota

D) Iowa

Diff: 1 Type: BI Var: 1

L.O.: 2.4.3

32) (58, 88, 94, 133, 185) is the five number summary for which state?

A) Kansas

B) Nebraska

C) South Dakota

D) Iowa

Diff: 2 Type: BI Var: 1

L.O.: 2.3.4;2.4.3

2.5 Two Quantitative Variables: Scatterplot and Correlation

Use the following to answer the questions below:

Identify which graphical display might be appropriate in each case. Select all that apply.

1) Investigate the number of Facebook friends students in your class have.

A) Histogram

B) Bar chart

C) Pie chart

D) Side-by-side bar chart

E) Segmented bar chart

F) Dotplot

G) Side-byside boxplots

H) Scatterplot

Diff: 2 Type: MC Var: 1

L.O.: 2.2.0

2) Compare the number of points scored for all games played in a season for all football teams in the Big 10 conference.

A) Side-by-side boxplots

B) Histogram

C) Bar chart

D) Pie chart

E) Side-by-side bar chart

F) Segmented bar chart

G) Dotplot

H) Scatterplot

Diff: 2 Type: MC Var: 1

L.O.: 2.4.3

3) Investigate the relationship between pulse rate (in beats per minute) and systolic blood pressure (the top number in a blood pressure reading, measured in of mercury) for patients at the student health center.

A) Scatterplot

B) Side-by-side boxplots

C) Histogram

D) Bar chart

E) Pie chart

F) Side-by-side bar chart

G) Segmented bar chart

H) Dotplot

Diff: 2 Type: MC Var: 1

L.O.: 2.5.0

4) Investigate the favorite type of music (country, rock, classical, etc.) for the students in your class.

A) Bar chart

B) Side-by-side boxplots

C) Histogram

D) Pie chart

E) Side-by-side bar chart

F) Segmented bar chart

G) Dotplot

H) Scatterplot

Diff: 2 Type: MC Var: 1

L.O.: 2.1.0

5) Compare the percentage of people in favor of Barack Obama and Mitt Romney in the 2012 Presidential election for the different regions in the U.S. (Northeast, Southeast, Midwest, West).

A) Side-by-side bar chart

B) Histogram

C) Bar chart

D) Pie chart

E) Segmented bar chart

F) Dotplot

G) Scatterplot

H) Side-by-side boxplots

Diff: 2 Type: MC Var: 1

L.O.: 2.1.0

6) Investigate the relationship between the length of the right foot (in cm) and the length of the right forearm (in cm) for students in your class.

A) Scatterplot

B) Side-by-side boxplots

C) Histogram

D) Bar chart

E) Pie chart

F) Side-by-side bar chart

G) Segmented bar chart

H) Dotplot

Diff: 2 Type: MC Var: 1

L.O.: 2.5.0

7) Investigate the length of songs on your iPod.

A) Side-by-side boxplots

B) Histogram

C) Bar chart

D) Pie chart

E) Side-by-side bar chart

F) Segmented bar chart

G) Dotplot

H) Scatterplot

Diff: 2 Type: MC Var: 1

L.O.: 2.2.0

8) Investigate the number of text messages sent yesterday by students in your class.

A) Side-by-side boxplots

B) Histogram

C) Bar chart

D) Pie chart

E) Side-by-side bar chart

F) Segmented bar chart

G) Dotplot

H) Scatterplot

Diff: 2 Type: MC Var: 1

L.O.: 2.2.0

9) Investigate the relationship between gender and left/right handedness for students in the class.

A) Side-by-side boxplots

B) Histogram

C) Bar chart

D) Pie chart

E) Side-by-side bar chart

F) Segmented bar chart

G) Dotplot

H) Scatterplot

Diff: 2 Type: MC Var: 1

L.O.: 2.1.0

10) Investigate the relationship between the number of hours of exercise per week and athlete or not for a sample of students at a small university.

A) Side-by-side boxplots

B) Histogram

C) Bar chart

D) Pie chart

E) Side-by-side bar chart

F) Segmented bar chart

G) Dotplot

H) Scatterplot

Diff: 2 Type: MC Var: 1

L.O.: 2.4.3

Use the following to answer the questions below:

Match the correlation to the corresponding scatterplot.

11) ________ 0.719

Diff: 1 Type: SA Var: 1

L.O.: 2.5.3

12) ________ -0.064

Diff: 1 Type: SA Var: 1

L.O.: 2.5.3

13) ________ 0.889

Diff: 1 Type: SA Var: 1

L.O.: 2.5.3

14) ________ -0.701

Diff: 1 Type: SA Var: 1

L.O.: 2.5.3

Use the following to answer the questions below:

A student working an independent research project wants to investigate if there is an association between the amount of sleep someone gets and their body mass index (BMI) - an indicator of body fatness. For a sample of 45 students, she records their BMI and the average amount of sleep they get on weeknights over a two-week period.

15) What would it mean for average amount of sleep and BMI to be positively correlated?

Diff: 2 Type: ES Var: 1

L.O.: 2.5.2

16) What would it mean for average amount of sleep to be negatively correlated with BMI?

Diff: 2 Type: ES Var: 1

L.O.: 2.5.2

17) Suppose the student found a correlation of -0.413 between amount of sleep and BMI. Would it be appropriate for her to conclude that getting more sleep causes individuals to have a lower BMI?

A) Yes

B) No

Diff: 2 Type: MC Var: 1

L.O.: 2.5.5

Use the following to answer the questions below:

The scatterplot shows the relationship between GPA and the number of Facebook friends for 30 students in a class.

18) Discuss the information contained in the scatterplot. What does it mean about GPA and number of Facebook friends?

Diff: 2 Type: ES Var: 1

L.O.: 2.5.1

19) For each corner of the scatterplot (top left, top right, bottom left, bottom right), describe a student whose responses place him or her in that corner.

Top Right: A student in this corner of the scatterplot would have a large number of Facebook friends (more than 1,000) and a high GPA (close to 4.0), i.e., a very strong student with lots of Facebook friends.

Bottom Left: A student in this corner of the scatterplot would have a small number of Facebook friends (less 200) and a low GPA (maybe 2.75 or less), i.e., a somewhat weak student with relatively few Facebook friends.

Bottom Right: A student in this corner of the scatterplot would have a large number of Facebook friends (more than 1,000) and a low GPA (maybe 2.75 or less), i.e., a somewhat weak student with lots of Facebook friends.

Diff: 2 Type: ES Var: 1

L.O.: 2.5.0

20) The correlation between GPA and the number of Facebook friends is -0.686. Should you go "unfriend" some of your Facebook friends if you want to improve your GPA (i.e., can you conclude that having more Facebook friends lowers GPA)?

A) Yes

B) No

Diff: 2 Type: MC Var: 1

L.O.: 2.5.5

2.6 Two Quantitative Variables: Linear Regression

Use the following to answer the questions below:

Trying to determine the number of students to accept is a tricky task for universities. The Admissions staff at a small private college wants to use data from the past few years to predict the number of students enrolling in the university from those who are accepted by the university. The data are provided in the following table.

1) What is the explanatory (X) variable?

A) Number of students accepted

B) Number of students enrolling

Diff: 2 Type: BI Var: 1

L.O.: 1.1.3;2.6.0

2) What is the response (Y) variable?

A) Number of students enrolling

B) Number of students accepted

Diff: 2 Type: BI Var: 1

L.O.: 1.1.3;2.6.0

3) Find the correlation between the number of students accepted and enrolled. Use two decimal places in your answer.

Diff: 2 Type: SA Var: 1

L.O.: 2.5.4

4) Find the least squares regression line for predicting the number enrolled from the number accepted.

A) = 89 + 0.208 accepted, where E = enrolled

B) = 85 + 0.208 accepted, where E = enrolled

C) = 89 + 0.204 accepted, where E = enrolled

D) = 85 + 0.206 accepted, where E = enrolled

Diff: 2 Type: BI Var: 1

L.O.: 2.6.1

5) Interpret the slope in of the least squares regression line in context.

Diff: 2 Type: ES Var: 1

L.O.: 2.6.3

6) Interpret the intercept of the least squares regression line in context. Does the interpretation make sense?

Diff: 2 Type: ES Var: 1

L.O.: 2.6.3;2.6.5

7) Suppose Admissions has announced that 2,575 students have been accepted this year. Use your regression equation to predict the number of students that will enroll.

= 89 + 0.208(2,575) = 624.6

The model predicts that if 2,575 are accepted, then 624.6 students will enroll at the college.

Diff: 2 Type: ES Var: 1

L.O.: 2.6.2

Use the following to answer the questions below:

The least squares regression line is displayed on the provided scatterplot. Note that the points are displayed with numbers (each point having its own number), rather than points.

8) Which point has the most extreme negative residual?

A) 0

B) 1

C) 4

D) 9

Diff: 3 Type: BI Var: 1

L.O.: 2.6.4

9) Which point has the most extreme positive residual?

A) 0

B) 4

C) 8

D) 9

Diff: 3 Type: BI Var: 1

L.O.: 2.6.4

10) Which point has the residual that is closest to 0?

A) 1

B) 4

C) 5

D) 9

Diff: 3 Type: BI Var: 1

L.O.: 2.6.4

Use the following to answer the questions below:

Students in a small statistics course collected data to determine if the length of the forearm could be used to predict the length of the foot (both measured in centimeters). Their data are displayed in the provided table.

11) Based on their goal (to predict foot length from forearm length), which variable is the explanatory variable?

A) Forearm length

B) Foot length

Diff: 2 Type: BI Var: 1

L.O.: 1.1.3;2.5.0;2.6.0

12) Which of the following would you expect to be true about the association between the length of the forearm and the length of the foot?

A) Positive association

B) Negative association

C) No association

Diff: 1 Type: BI Var: 1

L.O.: 2.5.2

13) A scatterplot of the data collected by the students is provided. Does there appear to be a positive or negative association between these two variables? What does this mean for these two variables?

A) Positive; This means that people with longer forearms tend to have larger feet.

B) Positive; This means that people with longer forearms tend to have smaller feet.

C) Negative; This means that people with longer forearms tend to have larger feet.

D) Negative; This means that people with longer forearms tend to have smaller feet.

Diff: 1 Type: BI Var: 1

L.O.: 2.5.1;2.5.2

14) Find the correlation between forearm and foot length. Use three decimal places in your answer.

Diff: 2 Type: SA Var: 1

L.O.: 2.5.4

15) If the forearm and foot lengths had been measured in inches instead of centimeters the correlation would be different.

Diff: 3 Type: TF Var: 1

L.O.: 2.5.3

16) Find the least squares regression equation for predicting foot length from forearm length.

A) y = foot;

= 9.216 + 0.5735 forearm

B) y = foot;

= 2.133 + 0.7246 forearm

C) y = foot;

= 2.133 + 0.5735 forearm

D) y = foot;

= 9.216 + 0.7246 forearm

Diff: 2 Type: BI Var: 1

L.O.: 2.6.1

17) A scatterplot of the data with the least squares regression line is shown. What are the coordinates of the point with the most extreme negative residual?

A) (28, 23)

B) (30, 23)

C) (32, 31)

D) (36, 29)

Diff: 2 Type: BI Var: 1

L.O.: 2.6.4

18) A scatterplot of the data with the least squares regression line is shown. What are the coordinates of the point with the most extreme positive residual?

A) (32, 31)

B) (30, 23)

C) (28, 23)

D) (23, 23)

Diff: 2 Type: BI Var: 1

L.O.: 2.6.4

19) Using your model to predict the foot length for an individual with a forearm length of 45 cm would be ________.

A) extrapolation

B) regression

C) a positive residual

D) a negative residual

Diff: 2 Type: BI Var: 1

L.O.: 2.6.5

Use the following to answer the questions below:

A biologist collected data on a sample of 20 porcupines. She wants to be able to predict the body mass of a porcupine (in grams) based on the length of the porcupine (in cm).

Her least squares regression equation is where M is the mass.

20) Interpret the slope of the least squares regression line, in the context of the situation.

Diff: 2 Type: ES Var: 1

L.O.: 2.6.3

21) If it would make sense, provide a clear interpretation of the intercept of the regression line, in context. Otherwise, explain why the interpretation does not make sense.

Diff: 2 Type: ES Var: 1

L.O.: 2.6.3;2.6.5

22) Predict the body mass of a porcupine that is 51 cm long. Report your answer using one decimal place.

A) 5,866.6 g

B) 5,661.0 g

C) 5,732.5 g

D) 6,139.2 g

Diff: 2 Type: BI Var: 1

L.O.: 2.6.2

23) One of the porcupines in the dataset had a body length of 51 cm and a body mass of 5,281 g. Calculate the residual for this porcupine. Use one decimal place in your calculation.

A) -585.6 g.

B) 585.6 g.

C) -451.5 g.

D) 451.5 g.

Diff: 2 Type: BI Var: 1

L.O.: 2.6.4

24) A scatterplot of the biologist's data, with the least squares regression line, is provided. There is a clear outlier in the lower left corner of the plot. How would removing this point from the dataset most likely affect the correlation between body length (cm) and body mass (g)?

A) It would make the correlation stronger.

B) It would make the correlation weaker.

C) It would have no impact on the correlation between body length and body mass.

Diff: 3 Type: BI Var: 1

L.O.: 2.5.6;2.6.6

25) Another variable that the biologist recorded was the chest circumference (in cm) of the porcupines. Explain what both a negative and a positive association between body mass and chest circumference would mean. Which is more plausible in this situation?

A negative correlation would mean that porcupines that have a larger chest circumference tend to have a lower body mass while those with the smaller chest circumference would tend to have a higher body mass.

The positive correlation is most plausible in this situation - the porcupines that are "bigger" in the chest area are likely bigger overall and thus should have the higher body mass.

Diff: 2 Type: ES Var: 1

L.O.: 2.5.2;2.5.3

2.7 Data Visualization and Multiple Variables

1) There are no testbank questions for this section.

Diff: 1 Type: SA Var: 1

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