Question

A population of size 320 has a proportion equal to .60 for the characteristic of interest. What are the mean and the standard deviation, respectively, of the sample proportion for samples of size 12?a. .60 and.02 b. 192 and 45 c. .60 and.14 d. 320 and.0

Answer 1

The answer is c.) 0.6 and 0.14

Explanation:

Given population has a size of 320.

The proportion of population = 0.6

The mean of population, p = 0.6

The mean of sample,
`\hat{p}`= 0.6

Therefore
`\hat{q}` = 1 -
`\hat{p}` = 1 - 0.6 = 0.4

The sample size = 12

Therefore the standard deviation of the sample,

`s = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n} } = \sqrt{(0.6 * 0.4)/(12) } = 0.1414`

The mean and the standard deviation for a sample size of 12 are 0.6 and 0.14 respectively.

The answer is c.) 0.6 and 0.14