Question

The following 5 questions are based on this information. An economist reports that 47% (p¯=0.47p¯=0.47) of a random sample of 1200 middle-income American households actively participate in the stock market. The goal is to construct a 95% confidence interval of the proportion (pp) of all middle-income Americans who actively participate in the stock market. The standard error (SE) of p¯p¯ is Select one:

a. 0.47
b. 0.047
c. 0.021
d. 0.014

Answer 1

Option D) 0.014

Explanation:

We are given the following in the question:

Sample size, n = 1200

Sample proportion =

`\hat{p} = 0.47`

We have to make a 95% confidence interval.

Formula for standard error:

`S.E = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

Putting the values, we get:

`S.E = \sqrt{(0.47(1-0.47))/(1200)} = 0.014`

Thus, the correct answer is

Option D) 0.014