To Plan the Budget for Next Year a College Needs $35 \%$

Multiple Choice

To plan the budget for next year a college needs to estimate what impact the 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 confidence interval be used to test the hypothesis $\mathrm { H } _ { 0 } : p = 0.35$ versus $\mathrm { H } _ { \mathrm { A } } : p \neq 0.35$ at the $\alpha = 0.10$ level of significance?

A) No, because they only used a sample of the applicants instead of all of them.
B) No, because financial aid amounts may not be normally distributed.
C) 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.
D) 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.
E) 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 increase.