Question

A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let ^ p denote the proportion in the sample who say they support the increase. Suppose that 47% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is

Answer 1

The correct response is "0.0129".

Explanation:

Given:

`n=1500`

`p=0.47`

`np=1500* 0.47`

`=705`

`nq=1500* (1-0.47)`

`=795`

Mean of sampling distribution will be:

`\mu_\hat{p}` =
`0.47`

hence,

The standard deviation will be:

⇒
`\sigma_\hat{p}` =
`\sqrt{(p(1-p))/(n) }`

By putting the values, we get

=
`\sqrt{(0.47(1-0.47))/(1500) }`

=
`0.012886686`

=
`0.0129`