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...
Me neither
i also do not know
if your coming from Mr browns stats class wassup
The correct answer is 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.
In hypothesis testing, we compare the value of the parameter (in this case, the proportion of students requiring financial aid) to a hypothesized value (in this case, p = 0.35). The confidence interval gives us a range of values within which we are 90% confident the true proportion lies. Since the hypothesized value of 0.35 falls within the confidence interval of (32%, 40%), we fail to reject the null hypothesis, suggesting that there is not strong evidence to indicate a change in the percentage of students requiring financial aid.
Options A, C, D, and E are incorrect because they either misinterpret the confidence interval or introduce irrelevant information not related to the hypothesis testing process.
To determine whether the confidence interval can be used to test the hypothesis, let's break down the information provided.
The null hypothesis (H0) in this case states that the proportion of students requiring financial aid (p) is equal to 0.35. The alternative hypothesis (Ha) states that the proportion of students requiring financial aid is not equal to 0.35.
The confidence interval provided is (32%, 40%). This interval was created using a random sample of this year's applications, and it indicates that we are 90% confident that the true proportion of students requiring financial aid falls within this range.
To test the hypothesis using the confidence interval, we need to check if the hypothesized proportion (0.35) falls within the confidence interval.
In this case, since 35% is in the confidence interval of (32%, 40%), it means that the hypothesized proportion falls within the range. Therefore, we fail to reject the null hypothesis.
Hence, the correct answer is 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.