Question

Construct a​ 95% confidence interval to estimate the population proportion using the data below.     xequals23 nequals95 Nequals500 The​ 95% confidence interval for the population proportion is (nothing comma nothing ). ​(Round to three decimal places as​ needed.)

Answer 1

95% Confidence interval: (0.1645,0.3197)

Explanation:

We are given the following in the question:

Sample size, n = 95

N = 500

x = 23

Finite population correction =

`=\sqrt{(N-n)/(N-1)} = \sqrt{(500-95)/(500-1)} = 0.9009`

`\hat{p} = (x)/(n) = (23)/(95) = 0.2421`

95% Confidence interval:

`\hat{p}\pm z_(stat)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}* fpc`

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

Putting the values, we get:

`0.2421\pm 1.96(\sqrt{(0.2421(1-0.2421))/(95)})* 0.9009 \\\\= 0.2421\pm 0.0776\\=(0.1645,0.3197)`