Question

The chamber of commerce in a beach resort town wants to estimate the proportion of visitors who are repeat visitors. From previous experience they believe the proportion is in the vicinity of 0.5 and they want to estimate the proportion to within3 percentage points with 95 percent confidence. What is the sample size they should​ use?

Answer 1

Answer: 1068

Explanation:

Formula of sample size :

`n=p(1-p)((z^c)/(E))^2` , where p = prior population proportion , E = margin of error ,
`z^c` = Critical z- value.

Let p = proportion of visitors who are repeat visitors.

Given : p=0.5

E= 3%= 0.03

critical z-value for 95% confidence = 1.96

Now,
`n=(0.5)(1-0.5)((1.96)/(0.03))^2`

`=0.25(65.33)^2\\\\=0.25(4268.0089)=1067.002225\approx1068` [round to the next integer]

Hence, the required sample size = 1068