We are interested in p, the population proportion of all people who are currently happy with their cell phone plans. In a small study done in 2012, it was found that in a sample of 150 people, there were 90 who were happy with their cell phone plans. Using the data from this prior study, find the sample size needed to construct a 95% confidence interval for p with a margin of error of 0.025
Accepted Solution
A:
Answer: 19Step-by-step explanation:The formula to find the sample size is given by :_[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})[/tex]Given : Significance level : [tex]\alpha:1-0.95=0.05[/tex]Critical value : [tex]z_{\alpha/2}=1.96[/tex]The estimated population proportion by using sample : [tex]p=\dfrac{90}{150}=0.6[/tex]Margin of error : E=0.025Now, the required sample size will be :-[tex]n=0.6(1-0.6)(\dfrac{(1.96)}{0.025})=18.816\approx19[/tex]