Question

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

Answer 1

Answer: 19

Explanation:

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

`n=p(1-p)((z_(\alpha/2))/(E))`

Given : Significance level :
`\alpha:1-0.95=0.05`

Critical value :
`z_(\alpha/2)=1.96`

The estimated population proportion by using sample :
`p=(90)/(150)=0.6`

Margin of error : E=0.025

Now, the required sample size will be :-

`n=0.6(1-0.6)(((1.96))/(0.025))=18.816\approx19`