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

Answer:

95% Confidence interval:  (0.361,0.539)    

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 120

Number of farmers who reusable cloth bags, x = 54

$\hat{p} = \dfrac{x}{n} = \dfrac{54}{120} = 0.45$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96$

Putting the values, we get:

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

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