Question

​It's believed that as many as 23​% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. What sample size would allow us to increase our confidence level to​ 95% while reducing the margin of error to only 3​%?

Answer 1

Answer: 756

Step-by-step explanation:

Given : The proportion of adults over 50 never graduated from high school.  = 0.23

Margin of error : E=0.03

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

The formula to find the sample size is given by:_

$n=p(1-p)(\dfrac{z_{\alpha/2}\ }{E})^2$

i.e. $n=(0.23)(0.77)(\dfrac{(1.96)}{0.03})^2=755.941511111approx756$

Hence, the required minimum sample size = 756