Question

A recent poll of 120 randomly selected adults who frequent the local​ farmer's market found that 54 have purchased reusable cloth bags for their groceries. What is the​ 95% confidence interval for the proportion of adults who have purchased reusable cloth​ bags?

Answer 1

95% Confidence interval: (0.361,0.539)

Explanation:

We are given the following in the question:

Sample size, n = 120

Number of farmers who reusable cloth bags, x = 54

`\hat{p} = (x)/(n) = (54)/(120) = 0.45`

95% Confidence interval:

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

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

Putting the values, we get:

`0.45\pm 1.96(\sqrt{(0.45(1-0.45))/(120)}) = 0.45\pm 0.089\\\\=(0.361,0.539)`

is the required 95% confidence interval for the proportion of adults who have purchased reusable cloth​ bags.