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 H0: µ1 = µ2 = µ3 = µ4 = µ5. 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 a = 0.05 level of significance.
(g) Use the one-way ANOVA procedure to determine if there is a difference in the mean time 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 = 0.05.

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Highly Selective Not Nonselective Open-door Selective Rated 5.1 2.5 4.6 4.7 5.9 5.1 4.3 2.3 4.2 4.3 4.3 4.4 4.3 6.4 4.4 4.8 4.0 4.2 5.6 3.8 55 5.1 4.1 6.0 4.7 5.0 2.6 3.1 4.7 4.5 4.1 3.8 4.2 73 5.5 3.4 5.2 5.7 5.6 5.5 4.3 4.5 2.3 6.9 4.6 4.5 3.9 4.0 5.1 4.1