Question

A dean at a large state university (student population exceeds 40,000) is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.

A. State the conditions that should be met to reliably estimate the proportion of students on financial aid using a confidence interval and explain whether or not they are met.

B. Find a point estimate for the proportion of students on financial aid and label your answer with the appropriate symbol.

C. Construct a 95% confidence interval estimate for the proportion of students on financial aid and identify the margin of error. Show your calculation(s).

D. Interpret the confidence interval estimate obtained in (c) in the context of this particular study.

E. When the dean repeated this study the next year, she used a sample of 256 students and obtained an interval estimate of 41.95% to 58.05%. What is the confidence level and how many students in the sample received financial aid? Show your calculation(s).

Answer 1

A. To conduct the Confidence interval, we need that distribution needs to be normal and &

Here sample size is too large so as per central limit theorem distribution is normal. So conditions are satisfied

b.

c. For 95% CI, z value is 1.96 as

So Margin of Error =

Hence CI=

d. The proportion of students who receive some sort of financial aid for the large state university will lie in the range of 0.5218 to 0.6582

e.