Provide an appropriate response.
-A university dean 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. If the dean wanted to estimate the proportion of all students receiving financial aid to within $3 \%$ with $90 \%$ reliability, how many students would need to be sampled?
A) 728
B) 176
C) 443
D) 22

Question

Quizplus · Accepted Answer

To estimate the proportion of students receiving financial aid to within $3\%$ with $90\%$ reliability, we use the formula for sample size in estimating proportions: $n = \frac{Z^2 \hat{p}(1-\hat{p})}{E^2}$, where $Z$ is the Z-score corresponding to the desired confidence level (for $90\%$, $Z = 1.645$), $\hat{p}$ is the sample proportion (in this case, $118/200 = 0.59$), and $E$ is the margin of error (in this case, $3\% = 0.03$). Plugging in the values: $n = \frac{1.645^2 \times 0.59 \times (1-0.59)}{0.03^2}$, which calculates to approximately 728.

Provide an Appropriate Response 3%3 \%3% With 90%90 \%90% Reliability, How Many Students Would Need to Be Sampled? A)

Provide an Appropriate Response $3 \%$ With $90 \%$ Reliability, How Many Students Would Need to Be Sampled?
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