Question

. A study was done on the proportion of cities that have private refuse collectors. The student wants the margin of error to be within 0.10 of the population proportion, the desired level of confidence is 90%, and no estimate is available for the population proportion. What is the required sample size? (Hint: Since, no estimate is available for the population proportion, use 0.5].

Answer 1

Answer: 68

Explanation:

As per given , we have

Margin of error : E= 0.10

Critical z-value for 90% confidence interval :
`z_(\alpha/2)=1.645`

Since , the estimate of true proportion is unknown , then

The formula to find the sample size :-

`n=0.25((z_(\alpha/2))/(E))^2\\\\ n=0.25((1.645)/(0.10))^2\\\\ n=67.650625\approx68`

The required minimum sample size= 68