The AP Statistics class at the Hallways School for Girls takes a random sample of 50 students (from the school population of 698) and asks them if they get enough sleep. 18 of the respondents say "yes."
a. Check that all conditions for using the normal approximation to the sampling distribution are met in this scenario.
b. Construct a 95% confidence interval for the proportion of students at the Hallways School for Girls that will say they get enough sleep
c. Before doing this poll, Anna hypothesized that only 25% of all Hallways girls will say they get enough sleep. Based on your data and answer from
part (a) do you think Anna's hypothesis should be rejected? Should it be accepted?
d. If 42% of all girls at Hallways School for Girls would actually say they get enough sleep, what is the probability of getting a sample with as few (or
fewer) "yes" answers as the AP class got?