Question

Suppose the U.S. president wants to estimate the proportion of the population that supports his current policy toward revisions in the health care system. The president wants the estimate to be within 0.03 of the true proportion. Assume a 99% level of confidence. The president’s political advisors found a similar survey from two years ago that reported that 62% of people supported health care revisions. (Answers must be whole numbers.)

How large of a sample is required?
How large of a sample would be necessary if no estimate were available for the proportion supporting current policy?

Answer 1

A sample size of approximately 1846 people is required for a 99% confidence level with a margin of error of 0.03, using a previous estimate of 62% support for healthcare revisions.

Step-by-step explanation:

To calculate the sample size required for estimating a population proportion with a certain level of confidence, we can use the formula for the sample size of a proportion:

n = (Z^2 × p × (1-p)) / E^2

Where:

• Z is the z-value corresponding to the confidence level
• p is the estimated proportion from previous research
• E is the margin of error

For a 99% confidence level, the Z value is approximately 2.576. Using a previous estimate of 62% support, p would be 0.62, and E would be 0.03 (the desired margin of error).

n = (2.576^2 × 0.62 × 0.38) / 0.03^2

After calculating, we determine that a sample size of approximately 1846 participants would be required. (Actual calculations may provide a slightly different number due to rounding.)

If no estimate is available, the most conservative estimate for p is 0.5, as it maximizes the product p(1-p).

n = (2.576^2 × 0.5 × 0.5) / 0.03^2

Using these values, the required sample size would be approximately 1842 participants.