Researchers at the University of Alaska have been trying to find inexpensive feed sources for Alaska reindeer growers (“Effects of Two Barley-Based Diets on Body Mass and Intake Rates of Captive Reindeer During Winter,” Poster Presentation: School of Agriculture and Land Resources Management, University of Alaska Fairbanks, 2002). They are focusing on Alaskagrown barley because commercially available feed supplies are too expensive for farmers. Typically, reindeer lose weight in the fall and winter, and the researchers are searching for a feed to minimize this loss. Thirteen pregnant reindeer were randomly divided into two groups to be fed on two different varieties of barley, thual and finaska. Here are the weight gains between October 1 and December 15 for the seven that were fed thual barley (T) and the six that were fed finaska barley (F).

The weight gains are all negative, indicating that all of the animals lost weight. The thual barley is less fibrous and more digestible, and the intake rates for the two varieties of barley were very nearly the same, so the experimenters expected less weight loss for the thual variety.

a. Determine 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 obtain 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 ofmeans.
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? Is it in the direction anticipated by the experimenters?

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T: -5.83 -11.5 -5.5 -1.33 -3.83 -3.33 -7.17 F: -0.17 -0.67 -4 -3 -1.33 -0.5