Question 2.1

Question 2.2

Question 2.3

Question 2.4

Question 2.5

Question 2.6

Question 2.7

Question 2.8

Question 2.9

Question 2.10

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Question 2.11

Question 2.12

Question 2.13

Question 2.14

Question 2.15

Question 2.16

Question 2.17

Question 2.18

Question 2.19

Question 2.20

Question 2.21

Question 2.22

On a test of marital satisfaction, scores could range from 0 to 27.

1. What is the full range of data, according to the calculation procedure described in this chapter?

2. What would the interval size be if we wanted six intervals?

3. List the six intervals.

Question 2.23

Question 2.24

Question 2.25

Question 2.26

Question 2.27

Question 2.28

Question 2.29

A researcher collects data on the ages of college students. As you have probably observed, the distribution of age clusters around 19 to 22 years, but there are extremes on both the low end (high school prodigies) and the high end (nontraditional students returning to school).

1. What type of skew might you expect for such data?

2. Do the skewed data represent a floor effect or a ceiling effect?

Question 2.30

If you have a Facebook account, you are allowed to have up to 5000 friends. At that point, Facebook cuts you off, and you have to “defriend” people to add more. Imagine you collected data from Facebook users at your university about the number of friends each has.

1. What type of skew might you expect for such data?

2. Do the skewed data represent a floor effect or ceiling effect?

Question 2.31

1. Using the following set of data, construct a single stem-and-leaf plot:
   

   

2. Refer to the stem-and-leaf plot you created for part (a). Does it depict a symmetric or a skewed distribution?

Question 2.32

1. Using the following set of data, construct a single stem-and-leaf plot:
   

   

2. Refer to the stem-and-leaf plot you created for part (a). Does it depict a symmetric or a skewed distribution?

Question 2.33

Frequency tables, histograms, and the National Survey of Student Engagement: The National Survey of Student Engagement (NSSE) surveys freshmen and seniors about their level of engagement in campus and classroom activities that enhance learning. Hundreds of thousands of students at almost 1000 schools have completed surveys since 1999, when the NSSE was first administered. Among the many questions, students were asked how often they were assigned a paper of 20 pages or more during the academic year. For a sample of 19 institutions classified as national universities that made their data publicly available through the U.S. News & World Report Web site, here are the percentages of students who said they were assigned between 5 and 10 twenty-page papers:

1. Create a frequency table for these data. Include a third column for percentages.

2. For what percentage of these schools did exactly 4% of the students report that they wrote between 5 and 10 twenty-page papers that year?

3. Is this a random sample? Explain your answer.

4. Create a histogram of grouped data, using six intervals.

5. In how many schools did 6% or more of the students report that they wrote between 5 and 10 twenty-page papers that year?

6. How are the data distributed?

Question 2.34

Frequency tables, histograms, and the Survey of Earned Doctorates: The Survey of Earned Doctorates regularly assesses the numbers and types of doctorates awarded at U.S. universities. It also provides data on the length of time in years that it takes to complete a doctorate. Below is a modified list of this completion-time data, truncated to whole numbers and shortened to make your analysis easier. These data have been collected every 5 years since 1982.

1. Create a frequency table for these data.

2. How many schools have an average completion time of 8 years or less?

3. Is a grouped frequency table necessary? Why or why not?

4. Describe how these data are distributed.

5. Create a histogram for these data.

6. At how many universities did students take, on average, 10 or more years to complete their doctorates?

Question 2.35

Frequency tables, histograms, polygons, and university acceptance rates: U.S. News and World Report publishes acceptance rates for U.S. universities. Following are the acceptance rates for the top 70 U.S. universities in 2011.

1. Create a grouped frequency table for these data.

2. The data have quite a range, with the highest acceptance rates among the top 70 belonging to Yeshiva University in New York, and the lowest belonging to Harvard University. What research hypotheses come to mind when you examine these data? State at least one research question that these data suggest to you.

3. Create a grouped histogram for these data. Be careful when determining the midpoints of your intervals!

4. Create a frequency polygon for these data.

5. Examine these graphs and give a brief description of the distribution. Are there unusual scores? Are the data skewed, and if so, in which direction?

Question 2.36

Frequency tables, histograms, and the basketball wins: Here are the number of wins for the 30 U.S. National Basketball Association teams for the 2012–2013 NBA season.

1. Create a grouped frequency table for these data.

2. Create a histogram based on the grouped frequency table.

3. Write a summary describing the distribution of these data with respect to shape and direction of any skew.

4. Here are the numbers of wins for the 8 teams in the National Basketball League (NBL) of Canada. Explain why we would not necessarily need a grouped frequency table for these data.

Question 2.37

Types of distributions: Consider these three variables: finishing times in a marathon, number of university dining hall meals eaten in a semester on a three-meal-a-day plan, and scores on a scale of extroversion.

1. Which of these variables is most likely to have a normal distribution? Explain your answer.

2. Which of these variables is most likely to have a positively skewed distribution? Explain your answer, stating the possible contribution of a floor effect.

3. Which of these variables is most likely to have a negatively skewed distribution? Explain your answer, stating the possible contribution of a ceiling effect.

Question 2.38

Type of frequency distribution and type of graph: For each of the types of data described below, first state how you would present individual data values or grouped data when creating a frequency distribution. Then, state which visual display(s) of data would be most appropriate to use. Explain your answers clearly.

1. Eye color observed for 87 people

2. Minutes used on a cell phone by 240 teenagers

3. Time to complete the London Marathon for the more than 35,000 runners who participate

4. Number of siblings for 64 college students

Question 2.39

Question 2.40

Question 2.41

Question 2.42

Frequencies, distributions, and numbers of friends: A college student is interested in how many friends the average person has. She decides to count the number of people who appear in photographs on display in dorm rooms and offices across campus. She collects data on 84 students and 33 faculty members. The data are presented below.

1. What kind of visual display is this?

2. Estimate how many people have fewer than 6 people pictured.

3. Estimate how many people have more than 18 people pictured.

4. Can you think of additional questions you might ask after reviewing the data displayed here?

5. Below is a subset of the data described here. Create a grouped frequency table for these data, using seven groupings.

   

6. Create a histogram of the grouped data from (e).

7. Describe how the data depicted in the original graph and the histogram you created in part (f) are distributed.

8. Use the data in part (e) to create a stem-and-leaf plot.

9. Refer to the stem-and-leaf plot you created in (h). Do these data reflect a floor effect or a ceiling effect? Explain your answer.

Question 2.43

Frequencies, distributions, and breast-feeding duration: The Centers for Disease Control and other organizations are interested in the health benefits of breast-feeding for infants. The National Immunization Survey includes questions about breast-feeding practices, including: “How long was [your child] breast-fed or fed breast milk?” The data for duration of breast-feeding, in months, for 20 hypothetical mothers are presented below.

1. Create a frequency table for these data. Include a third column for percentages.

2. Create a histogram of these data.

3. Create a frequency polygon of these data.

4. Create a grouped frequency table for these data with three groups (create groupings around the mid-points of 2.5 months, 7.5 months, and 12.5 months).

5. Create a histogram of the grouped data.

6. Create a frequency polygon of the grouped data.

7. Write a summary describing the distribution of these data with respect to shape and direction of any skew.

8. If you wanted the data to be normally distributed around 12 months, how would the data have to shift to fit that goal? How could you use knowledge about the current distribution to target certain women?

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Question 2.44

Developing research ideas from frequency distributions: Below are frequency distributions for two sets of the friends data described in Exercise 2.42, one for the students and one for the faculty members studied.

1. How would you describe the distribution for faculty members?

2. How would you describe the distribution for students?

3. If you were to conduct a study comparing the numbers of friends that faculty members and students have, what would the independent variable be and what would be the levels of the independent variable?

4. In the study described in (c), what would the dependent variable be?

5. What is a confounding variable that might be present in the study described in (c)?

6. Suggest at least two additional ways to operationalize the dependent variable. Would either of these ways reduce the impact of the confounding variable described in (e)?

Question 2.45

Frequencies, distributions, and graduate advising: In a study of mentoring in chemistry fields, a team of chemists and social scientists identified the most successful U.S. mentors—professors whose students were hired by the top 50 chemistry departments in the United States (Kuck et al., 2007). Fifty-four professors had at least three students go on to such jobs. Here are the data for the 54 professors. Each number indicates the number of students successfully mentored by each different professor.

1. Construct a frequency table for these data. Include a third column for percentages.

2. Construct a histogram for these data.

3. Construct a frequency polygon for these data.

4. Describe the shape of this distribution.

5. How did the researchers operationalize the variable of mentoring success? Suggest at least two other ways in which they might have operationalized mentoring success.

6. Imagine that researchers hypothesized that an independent variable—the number of publications coauthored by the advisor—predicts the dependent variable of mentoring success. One professor, Dr. Yuan T. Lee, from the University of California at Berkeley, trained 13 future top faculty members. Dr. Lee won a Nobel Prize. Explain how such a prestigious and public accomplishment might present a confounding variable to the hypothesis described above.

7. Dr. Lee had many students who went on to top professorships before he won his Nobel Prize. Several other chemistry Nobel Prize winners in the United States serve as graduate advisors but have not had Dr. Lee’s level of success as mentors. What are other possible variables that might predict the dependent variable of attaining a top professor position?