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

Answer:

$n\geq 2400$

Step-by-step explanation:

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

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}\leq 0.01\\\\\\\\\sqrt{\frac{0.4\times0.6}{n}}\leq 0.01$

#We take square root on both sides:

$\frac{0.4\times0.6}{n}\leq 0.01^2\\\\\\n\geq {\frac{0.4\times0.6}{0.01^2}\\\\n\geq 2400$

Hence, the sample size must at least 2400