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Suppose the U.S. president wants an estimate of the

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Suppose the U.S. president...

Suppose the U.S. president wants an estimate of the proportion of the population who
support his current policy toward revisions in the health care system. The president wants
the estimate to be within .04 of the true proportion. Assume a 95 percent level of confidence.
The president’s political advisors estimated the proportion supporting the current
policy to be .60.
a. How large of a sample is required?
b. How large of a sample would be necessary if no estimate were available for the proportion
supporting current policy?

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Submitted: 10 months ago.Category: Calculus and Above
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9/25/2017
Tutor: Ryan, Engineer replied 10 months ago
Ryan
Ryan, Engineer
Category: Calculus and Above
Satisfied Customers: 9,184
Experience: B.S. in Civil Engineering
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Hi,

Thank you for using the site. I will be happy to help you with these problems.

For a 95% confidence level, use z = 1.96.

For part a: n = (p)(1 - p)(z / E)^2 = (0.6)(1 - 0.6)(1.96 / 0.04)^2 = 576.24 --> 577

For part b: use p = 0.5 since there is no estimate for the proportion supporting the current policy.

n = (0.5)(1 - 0.5)(1.96 / 0.04)^2 = 600.25 --> 601

Note that the calculated sample size is always rounded up to the next whole number, even when the decimal portion is less than 0.5. This is because the calculated amount is a minimum value, but the sample size must also be an integer. If the sample size was rounded down instead of up it would not meet the minimum requirement.

Please feel free to ask if you have any additional questions about these solutions.

Thanks,

Ryan

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