Question

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: seven percentage points, confidence level 95%, from a prior study,^p is estimated by the decimal equivalent of 42%n=_____ (round to the nearest integer.)

Answer 1

Answer: 191

Step-by-step explanation:

Formula to find the minimum sample size required to estimate a population proportion or percentage:

$n= \hat{p}(1-\hat{p})(\dfrac{z^*}{E})^2$

, where $\hat{p}$ = proportion estimated by prior study.

E= Margin of error.

z* = Critical z-value.

Given : Confidence level = 95%

Critical value for 95% confidence = z*=1.96

$\hat{p}=\ 42\%=0.42$

E= 7%= 0.07

Then, $n= 0.42(1-0.42)(\dfrac{1.96}{0.07})^2$

$n= 0.42(0.58)(28)^2$

$n= 0.2436(784)=190.9824approx191$

Hence, the minimum sample size required=191