# Chapter 7 - Estimates and Sample Sizes - 7-2 Estimating a Population Proportion - Basic Skills and Concepts: 35

a) 271 b)139 c)No.

#### Work Step by Step

If $\hat{p}$ is known:$n=\frac{z^2_{\frac{\alpha}{2}}\cdot \hat{p}\cdot (1-\hat{p})}{E^2}.$ If $\hat{p}$ is unknown:$n=\frac{z^2_{\frac{\alpha}{2}}\cdot0.25}{E^2}.$ a) Here, $\hat{p}$ is unknown, hence $n=\frac{1.645^2\cdot0.25}{0.05^2}=271.$ b)Here, $\hat{p}$ is known, it is 85%=0.85, hence $n=\frac{1.645^2\cdot(0.85)\cdot(1-0.85)}{0.05^2}=139.$ c)This survey uses a convenience sample, whoch doesn't represent the entire population correctly.

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