Question

According to Gallup, 58% of US Adults choose to pursue higher education solely to get a good job. Consider taking samples of 900 adults in the United States and calculating the sample proportion who pursue higher education solely to get a good job.

Assuming all conditions are met, fill in the blanks for the following about the sampling distribution for the sample proportion.
The sampling distribution for the sample proportion follows the [ Select ] ["Population Model", "Sample Model", "Random Model", "Normal Model"] . The mean of the sampling distribution is [ Select ] ["0.064", "0.0165", "900", "0.58"] . The standard deviation of the sampling distribution is [ Select ] ["0.58", "0.064", "900", "0.0165"]

Answer 1

(a) Normal model

`(b)\ Mean = 0.58`

`(c)\ \sigma = 0.0165`

Explanation:

Given

`p = 58\%`

`n = 900`

Solving (a): The distribution type

The sample follows a normal model

Solving (b): The mean

This is calculated as:

`Mean = p`

So, we have:

`Mean = 58\%`

Express as decimal

`Mean = 0.58`

Solving (c): The standard deviation

This is calculated as:

`\sigma = \sqrt{(p(1 - p))/(n)}`

So, we have:

`\sigma = \sqrt{(58\%(1 - 58\%))/(900)}`

Express as decimals

`\sigma = \sqrt{(0.58(1 - 0.58))/(900)}`

`\sigma = \sqrt{(0.58 * 0.42)/(900)}`

`\sigma = \sqrt{(0.2436)/(900)}`

`\sigma = √(0.00027066666)`

`\sigma = 0.0165`