According to a Monitoring the Future, 53% of twelfth-graders actively participate in sports, athletics, or exercising on a nearly daily basis. The Arkansas Department of Health selected a simple random sample of 2,382 twelfth-grade students and asked them whether or not they actively participated in sports, athletics, or exercising on a nearly daily basis. ADH is interested in the difference between the proportion of eighth graders and twelfth graders that exercise on a daily basis.
a) What is the shape of the sampling distribution of the difference between the sample proportions of eighth graders and twelfth graders that exercise on a daily basis? Justify.
b) What are the mean and standard deviation of the sampling distribution of the difference between the sample proportions of eighth graders and twelfth graders (8th grade minus 12th grade)?
c) ADH found that of the twelfth graders sampled, 1,320 said they exercise on a daily basis. What is the sampling result of the difference between eighth graders and twelfth graders? Use the 8th grade data from question one on the front side of this page to answer this question.
d) Assuming the population probabilities are true, what is the probability of getting your result from part c, or less?
