Putting It Together: Time to Complete a Degree A researcher wanted to determine if the mean time to complete a bachelor’s degree was different depending on the selectivity of the first institution of higher education that was attended. The following data represent a random sample of 12th-graders who earned their degree within eight years. Probability plots indicate that the data for each treatment level are normally distributed.

(a) What type of observational study was conducted? What is the response variable?

(b) Find the sample mean for each treatment level.

(c) Find the sample standard deviation for each treatment level. Using the general rule presented in this chapter, does it appear that the population variances are the same?

(d) Use the time to degree completion for students first attending highly selective institutions to construct a 95% confidence interval estimate for the population mean.

(e) How many pairwise comparisons are possible among the treatment levels?

(f) Consider the null hypothesis . If we test this hypothesis using t-tests for each pair of treatments, use your answer from part (e) to compute the probability of making a Type I error, assuming that each test uses an  level of significance.

(g) Use the one-way ANOVA procedure to determine if there is a difference in the meantime to degree completion for the different types of initial institutions. If the null hypothesis is rejected, use Tukey’s test to determine which pairwise differences are significant using a familywise error rate of .

A study by the Organization for Economic Cooperation and Development (OECD) found that the average annual hours actually worked per worker has decreased in most of Western Europe in the first decade of the 2000s. Suppose an OECD-wide survey is conducted that found that 43% of the responding workers in the survey cited ‘less business, less work’ as the number one reason for this reduction in the annual working hours. Suppose you want to test this figure in the Netherlands to determine whether Dutch workers feel the same way. A random sample of 315 Dutch full-time workers whose work-week has been getting shorter is chosen. They are offered a selection of possible reasons for this reduction and 120 pick ‘less business, less work’. Use techniques presented in this chapter and an alpha of 0.05 to test to determine whether the 43% figure for Western Europe for this reason holds true in the Netherlands.