Question
6.32
Normal distributions in real life: Many variables are normally distributed, but not all are. (Fortunately, the central limit theorem saves us when we conduct research on samples from nonnormal populations if the samples are larger than 30!) Which of the following are likely to be normally distributed, and which are likely to be nonnormal? Explain your answers.
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Question
6.33
Distributions and getting ready for a date: We asked 150 students in our statistics classes how long, in minutes, they typically spend getting ready for a date. The scores ranged from 1 minute to 120 minutes, and the mean was 51.52 minutes. Here are the data for 40 of those students:
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Question
6.34
z scores and the GRE: By design, the verbal sub-test of the GRE has a population mean of 500 and a population standard deviation of 100 (the quantitative subtest has the same mean and standard deviation).
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- RyvmTSQkKVp3v7mANFAF809Vf0gIOLXwn7OApT7a6qWEHIjibUVgN/XcLvSwbI4UGwZ707NAGFLGxlfnffuwelfxi7OuWt/uxY5Koy/KNZs/qyLkgC0DpW86HarlNJxgwJyxIA==
- 7Mi7jqQbIEeuInbX/seVqhTuauH+PolFG5brCLgpNLOh9+Wg8cogFqpL/gZ77EA+M0KTv54ZMNO9zGvP22vbIs7xAI4nYxuIdG9hJDA9/gLohoEtm1d7Qt+f3F32a9C2QGdEPw==
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Question
6.35
The z distribution and hours slept: A sample of 150 statistics students reported the typical number of hours that they sleep on a weeknight. The mean number of hours was 6.65, and the standard deviation was 1.24. (For this exercise, treat this sample as the entire population of interest.)
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- 5+SN/bB3Sggv/e/z8EchRL0al63taOhjGysDUh7vPX/HiDZV152lBXDD0oW0NUOm6W0WEx2k/zPQ/7VQb/tfiRIywkbjz1sCS9/Pb5oGHdUZjefIwcKTjem0pImWbouY
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Question
6.36
The z distribution applied to admiration ratings: A sample of 148 of our statistics students rated their level of admiration for Hillary Clinton on a scale of 1 to 7. The mean rating was 4.06, and the standard deviation was 1.70. (For this exercise, treat this sample as the entire population of interest.)
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Question
6.37
z statistics and CFC scores: We have already discussed summary parameters for CFC scores for the population of participants in a study by Adams (2012). The mean CFC score was 3.20, with a standard deviation of 0.70. (Remember that we treated the sample of 800 participants as the entire population.) Imagine that you randomly selected 40 people from this population and had them watch a series of videos on financial planning after graduation. The mean CFC score after watching the video was 3.62.
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Question
6.38
Converting z scores to raw CFC scores: A CFC study found a mean CFC score of 3.20, with a standard deviation of 0.70, for the 800 students in the sample (Adams, 2012).
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Question
6.39
The normal curve and real-life variables: For each of the following variables, state whether the distribution of scores would likely approximate a normal curve. Explain your answer.
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- 1FQRqkDkSFTVNUSV9PrEGHZRZWy5CKF5AEB0sZZaxQBz4OofakBnCI8B2tXNYuI9
Question
6.40
Percentiles and eating habits: As noted in How It Works 6.1, Georgiou and colleagues (1997) reported that college students had healthier eating habits, on average, than did those who were neither college students nor college graduates. The 412 students in the study ate breakfast a mean of 4.1 times per week, with a standard deviation of 2.4. (For this exercise, again imagine that this is the entire population of interest.)
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Question
6.41
z scores and comparisons of sports teams: A common quandary faces sports fans who live in the same city but avidly follow different sports. How does one determine whose team did better with respect to its league division? In 2012, the Atlanta Braves baseball team and the Atlanta Falcons football team both did well. The Braves won 94 games and the Falcons won 13. Which team was better in 2012? The question, then, is: Were the Braves better, as compared to the other teams in Major League Baseball (MLB), than the Falcons, as compared to the other teams in the National Football League (NFL)? Some of us could debate this for hours, but it’s better to examine some statistics. Let’s operationalize performance over the season as the number of wins during regular season play.
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Question
6.42
z scores and comparisons of admiration ratings: Our statistics students were asked to rate their admiration of Hillary Clinton on a scale of 1 to 7. They also were asked to rate their admiration of actor, singer, and former American Idol judge Jennifer Lopez and their admiration of tennis player Venus Williams on a scale of 1 to 7. As noted earlier, the mean rating of Clinton was 4.06, with a standard deviation of 1.70. The mean rating of Lopez was 3.72, with a standard deviation of 1.90. The mean rating of Williams was 4.58, with a standard deviation of 1.46. One of our students rated her admiration of Clinton and Williams at 5 and her admiration of Lopez at 4.
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Question
6.43
Raw scores, z scores, percentiles, and sports teams: Let’s look at baseball and football again. We’ll look at data for all of the teams in Major League Baseball (MLB) and the National Football League (NFL), respectively.
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Question
6.44
Distributions and life expectancy: Researchers have reported that the projected life expectancy for South African men diagnosed with human immunodeficiency virus (HIV) at age 20 who receive anti-retroviral therapy (ART) is 27.6 years (Johnson et al., 2013). Imagine that the researchers determined this by following 250 people with HIV who were receiving ART and calculating the mean.
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Question
6.45
Distributions, personality testing, and depression: The revised version of the Minnesota Multiphasic Personality Inventory (MMPI-2) is the most frequently administered self-report personality measure. Test-takers respond to more than 500 true/false statements, and their responses are scored, typically by a computer, on a number of scales (e.g., hypochondriasis, depression, psychopathic deviation). Respondents receive a T score on each scale that can be compared to norms. (You’re likely to encounter T scores if you take psychology classes, but it’s good to be aware that they are different from the t statistic that you will learn about in a few chapters.) T scores are another way to standardize scores so that percentiles and cutoffs can be determined. The mean T score is always 50, and the standard deviation is always 10. Imagine that you administer the MMPI-2 to 95 respondents who have recently lost a parent; you wonder whether their scores on the depression scale will be, on average, higher than the norms. You find a mean score on the depression scale of 55 in your sample.
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Question
6.46
Distributions, personality testing, and social introversion: See the description of the MMPI-2 in Exercise 6.45. The mean T score is always 50, and the standard deviation is always 10. Imagine that you administer the MMPI-2 to 50 respondents who do not use Instagram or any other social media; you wonder whether their scores on the social introversion scale will be, on average, higher than the norms. You find a mean score on the social introversion scale of 60 in your sample.
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Question
6.47
Distributions and the General Social Survey: The General Social Survey (GSS) is a survey of approximately 2000 adults conducted each year since 1972, for a total of more than 38,000 participants. During several years of the GSS, participants were asked how many close friends they have. The mean for this variable is 7.44 friends, with a standard deviation of 10.98. The median is 5.00 and the mode is 4.00.
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Question
6.48
A distribution of scores and the General Social Survey: Refer to Exercise 6.47. Again, pretend that the GSS sample is the entire population of interest.
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Question
6.49
A distribution of means and the General Social Survey: Refer to Exercise 6.47. Again, pretend that the GSS sample is the entire population of interest.
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Question
6.50
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