A student project by Heather Kral studied students on “lifestyle floors” of a dormitory in comparison to students on other floors. On a lifestyle floor the students share a common major, and there are a faculty coordinator and resident assistant from that department. Here are the GPAs of 30 students on lifestyle floors (L) and 30 students on other floors (N):

Notice that the lifestyle GPAs have a large number of repeats and the distribution is skewed, so there is some question about normality.
a. Obtain a 95% confidence interval for the difference of population means using the two-sample t interval.

b. Use software to generate a bootstrap sample of differences of means. Check the bootstrap distribution for normality using a normal probability plot.
c. Use the standard deviation of the bootstrap distribution along with the mean and t critical value from (a) to get a 95% confidence interval for the difference of means.
d. Use the bootstrap sample and the percentile method to obtain a 95% confidence interval for the difference of means.
e. Compare your three confidence intervals. If they are very similar, why do you think this is the case?
f. Interpret your results. Is there a substantial difference between lifestyle and other floors? Why do you think the difference is as big as it is?

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L: N: 2.00 2.25 2.60 2.90 3.00 3.00 3.00 3.20 3.20 3.25 3.30 3.30 3.50 3.60 3.60 3.70 3.75 3.75 3.80 3.90 4.00 4.00 4.00 4.00 1.20 2.00 2.29 2.45 2.50 2.50 2.65 2.70 2.75 2.86 2.90 3.00 3.56 3.60 2.75 2.79 3.07 3.10 3.70 3.75 3.80 3.00 3.00 3.32 3.50 3.79 3.80 2.50 2.80 2.80 3.25 3.50 4.00 2.50 2.80 3.54