MATH SOLVE

4 months ago

Q:
# When designing a study to determine this proportion, what is the minimum number of drivers you would survey to be 95% confident that the population proportion is estimated to within 0.05?

Accepted Solution

A:

Answer: 385Step-by-step explanation:If the prior estimate of population proportion is unknown , then the formula to find the minimum sample size is given by :-[tex]n=0.25(\dfrac{z_{\alpha/2}}{E})^2[/tex]where, [tex]z_{\alpha/2}[/tex] is the z-value for significance level([tex]\alpha[/tex]) and E = the margin of error .Given : Confidence level = 0.95 significance level : [tex]\alpha=1-0.95=0.05[/tex]Critical z-value for 95% confidence level : [tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]Margin of error : E= 0.05Also, prior population proportion is unknown.Required sample size : [tex]n=0.25(\dfrac{1.96}{0.05})^2[/tex]Simplify , [tex]n=384.16\approx385[/tex]Hence,You would survey 385 drivers.