The article “Selected Characteristics of High-Risk Students and Their Enrollment Persistence” (Journal of College Student Development [1994]: 54–60) examined factors that affect whether students stay in college. The following summary statistics are based on data from a sample of 44 students who did not return to college after the first quarter (the nonpersisters) and a sample of 257 students who did return (the persisters):

a. Consider the 44 nonpersisters as a random sample from the population of all nonpersisters at the university where the data were collected. Compute a 98% confidence interval for the mean number of hours worked per week for nonpersisters.

b. Consider the 257 persisters as a random sample from the population of all persisters at the university where the data were collected. Compute a 98% confidence interval for the mean number of hours worked per week for persisters.

c. The 98% confidence interval for persisters is narrower than the corresponding interval for nonpersisters, even though the standard deviation for persisters is larger than that for nonpersisters. Explain why this happened.

d. Based on the interval in Part (a), do you think that the mean number of hours worked per week for nonpersisters is greater than 20? Explain.

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Number of Hours Worked per Week During the First Quarter Nonpersisters Persisters Mean 25.62 18.10 Standard Deviation 14.41 15.31