At Westville High School there are 315 seniors and 389 juniors. 65% of the seniors have parking
passes and 42% of the juniors have parking passes. The statistics teacher selects a SRS of 30
seniors and a separate SRS of 30 juniors. Let p hat s - p hat j , be the difference in the sample
proportions of
seniors and juniors that have parking passes.
a. What is the shape of the sampling distribution of p hat s - p hat j? Why?
b. Find the mean of the sampling distribution.
c. Calculate and interpret the standard deviation of the sampling distribution.
d. What is the probability that the difference in sample proportions (senior - junior) of students
with parking passes is greater than 30%?