Question

During routine​ conversations, the CEO of a new​ start-up reports that 15​% of adults between the ages of 21 and 39 will purchase her new product. Hearing​ this, some investors decide to conduct a​ large-scale study, hoping to estimate the proportion to within 5​% with 90​% confidence. How many randomly selected adults between the ages of 21 and 39 must they​ survey?

The number of adults that should be surveyed is ------. ​(Round up to the nearest whole​ number.)

Answer 1

Given : Margin of error=E=5%=0.05

Significance level=0.10

Estimate of the sample proportion=$\hat{p}$=15%=0.15

Now , the critical value is , $Z_{\alpha/2}=Z_{0.10/2}=1.645$ ; From Z-table

Therefore , the required sample size is ,

1.6452 * 0.15(1 – 0.15) n = Z2/2 *P(1-P) E2 138 0.052

Therefore , The number of adults that should be surveyed is 138.