To plan the budget for next year a college needs to estimate what impact current economic downturn might have on student requests for financial aid. Historically, this college has provided aid to 35% of its students. Officials look at a random sample of this year’s applications to see what proportion indicate a need for financial aid. Based on these data they create a 90% confidence interval of (32%, 40%).
Could this interval be used to test the hypothesis versus H0: p = 0.35 versus Ha: p ≠ 0.35 at the α = 0.10 level of significance?
A) Yes; since 35% is in the confidence interval they accept the null hypothesis, concluding that the percentage of students requiring financial aid will stay the same.
B) Yes; since 35% is in the confidence interval they fail to reject the null hypothesis, concluding that there is not strong evidence of any change in financial aid requests.
C) Yes; since 35% is not at the center of the confidence interval they reject the null hypothesis, concluding that the percentage of students requiring aid will change.
D) No, because financial aid amounts may not be normally distributed.
E) No, because they only used a sample of the applicants instead of all of them.
I have no idea...