1: When she was in junior high school, Elizabeth Likens started listening to classical music after she was told that "studies show that students who listen to classical music get better grades." What would you advise?
2: A random sample of 800 first-year students at a large university included 558 students who had attended public high schools and 242 who had attended private schools. The average grade point average (GPA) was 3.52 for students from public schools and 3.26 for students from private schools. Does the observed difference seem substantial? The author calculated the P value to be 0.10 and concluded that although "this study proved the null hypothesis to be true,.the sample size is minuscule in comparison to the population." Did she prove the null hypothesis to be true? Are her results invalidated by the small sample size?
3: A test of the null hypothesis that the average college student gains 15 pounds during the first year at college surveyed a random sample of 100 students and obtained a sample mean of 4.82 pounds with a standard deviation of 5.96 pounds. Explain why you either agree or disagree with each of these conclusions:
a. "We assumed that the standard deviation of our sample equaled the population standard deviation."
b. "We calculated the t value to be 17.08. The two-sided P value is 2.82 10 31. According to Fisher's rule of thumb, our data are not statistically Chapter 7 • Hypothesis Testing 215 significant because our P value is considerably less than 0.05. This indicates that the probability of observing a large difference between the sample mean and the null hypothesis is greater than 0.05."
c. "Our data strongly indicate that the Freshman 15 is just a myth. However, it must be recognized that we only took one sample of 100 students. Perhaps, if we took other samples, our results would be different.
4: Researchers used a random sample of size 100 to test the null hypothesis that the average difference between the household income of immigrant women and their adult daughters is equal to 0. Their decision rule was to reject the null hypothesis if the two-sided P value is less than a. Suppose that the population mean is, in fact, $500 and the standard deviation is known to be $5000. Calculate the probability that they will
a. reject the null hypothesis if a = 0.05. If a = 0.01.
b. not reject the null hypothesis if a = 0.05. If a = 0.01.