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A survey firm wants to ask a random sample of adults in Ohio if they support an increase
Chapter 12, Problem AP4.11(choose chapter or problem)
A survey firm wants to ask a random sample of 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 \(\hat{p}\) denote the proportion in the sample who say that they support the increase. Suppose that 40% of all adults in Ohio support the increase. How large a sample would be needed to guarantee that the standard deviation of \(\hat{p}\) is no more than 0.01?
(a) 1500
(b) 2400
(c) 2401
(d) 2500
(e) 9220
Questions & Answers
QUESTION:
A survey firm wants to ask a random sample of 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 \(\hat{p}\) denote the proportion in the sample who say that they support the increase. Suppose that 40% of all adults in Ohio support the increase. How large a sample would be needed to guarantee that the standard deviation of \(\hat{p}\) is no more than 0.01?
(a) 1500
(b) 2400
(c) 2401
(d) 2500
(e) 9220
ANSWER:Step 1 of 3
The standard deviation of the estimated proportion is given by
\(S D=\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}\) (i)
Since 40% of all adults in Ohio support the increase, therefore, true proportion \(\bar{p}=0.4\).
Plugging into equation (i),
\(S D=\sqrt{\frac{0.4(1-0.4)}{n}}\)