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Credit-Card Debt A school administrator is concerned about
Chapter 5, Problem 36AYU(choose chapter or problem)
A school administrator is concerned about the amount of credit-card debt that college students have. She wishes to conduct a poll to estimate the percentage of fulltime college students who have credit-card debt of $2000 or more. What size sample should be obtained if she wishes the estimate to be within 2.5 percentage points with 94% confidence if
(a) a pilot study indicates that the percentage is 34%?
(b) no prior estimates are used?
Questions & Answers
QUESTION:
A school administrator is concerned about the amount of credit-card debt that college students have. She wishes to conduct a poll to estimate the percentage of fulltime college students who have credit-card debt of $2000 or more. What size sample should be obtained if she wishes the estimate to be within 2.5 percentage points with 94% confidence if
(a) a pilot study indicates that the percentage is 34%?
(b) no prior estimates are used?
ANSWER:Step 1 of 2
(a) a pilot study indicates that the percentage is 34%
The sample size required to obtain a confidence interval for with a margin of error is given by
\(n=\widehat{p}(1-\widehat{p})\left[\frac{Z \alpha / 2}{E}\right]^{2}\)
Using \(\widehat{p}=\frac{34}{100}=0.34\) , \(E=2.5 \%=\frac{2.5}{100}=0.025\) and the Z-score corresponding to 94%
confidence level is 1.88.
\(\begin{aligned} n & =0.34(1-0.34)\left[\frac{1.88}{0.025}\right]^{2} \\ n & =0.34(0.66)\left[\frac{1.88}{0.025}\right]^{2} \\ \mathrm{n} & =1268.9909 \approx 1269 \end{aligned}\)