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 interval be used to test the hypothesis H
0:
p = 0.35 versus H
A:
p ≠ 0.35 at the α = 0.10 level of significance?
▸ 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.
▸ 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.
▸ No, because they only used a sample of the applicants instead of all of them.
▸ 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.
▸ No, because financial aid amounts may not be normally distributed.
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