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 24% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is . Round your answer to four decimal places.

Answer 1

Answer: The standard deviation of the sampling distribution is 0.0110

Step-by-step explanation:

The standard deviation of the sampling distribution is given by :-

$s=\sqrt{\dfrac{p(1-p)}{n}}$

, where p =  population proportion and n = sample size.

Let $\hat{p}$ denote the proportion in the sample who say they support the increase.

As per given :

$\hat{p}=24\%=0.24$

Then , the standard deviation of the sampling distribution is

$s=\sqrt{\dfrac{0.24(1-0.24)}{1500}}=\sqrt{0.0001216}\approx0.0110$

Hence, the standard deviation of the sampling distribution is 0.0110.