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

Answer:

The correct response is "0.0129".

Step-by-step explanation:

Given:

$n=1500$

$p=0.47$

$np=1500\times 0.47$

    $=705$

$nq=1500\times (1-0.47)$

    $=795$

Mean of sampling distribution will be:

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

hence,

The standard deviation will be:

⇒  $\sigma_\hat{p}$ = $\sqrt{\frac{p(1-p)}{n} }$

By putting the values, we get

         = $\sqrt{\frac{0.47(1-0.47)}{1500} }$

         = $0.012886686$

         = $0.0129$