Question

A one-question survey is to be distributed to a random sample of 1500 adults in Ohio. The question asks if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. How large of a sample would be needed to guarantee that the standard deviation, , is no more than 0.01.

Answer 1

`n\geq 2400`

Explanation:

-The standard deviation of the estimated proportion that is less than or equal to 1% is calculated as follows:

`\sigma_(\hat p)=\sqrt{(p(1-p))/(n)}\leq 0.01\\\\\\\\\sqrt{(0.4*0.6)/(n)}\leq 0.01`

#We take square root on both sides:

`(0.4*0.6)/(n)\leq 0.01^2\\\\\\n\geq {(0.4*0.6)/(0.01^2)\\\\n\geq 2400`

Hence, the sample size must at least 2400