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 34% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is

Answer 1

Answer:

The standard deviation of the sampling distribution is 0.0122 = 1.22%

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

A survey asks a random sample of 1500 adults in Ohio

This means that $n = 1500$

34% of all adults in Ohio support the increase.

This means that $p = 0.34$

The standard deviation of the sampling distribution is

$s = \sqrt{\frac{0.34*0.66}{1500}} = 0.0122$

The standard deviation of the sampling distribution is 0.0122 = 1.22%