Question

Construct the 99% confidence interval estimate of the population proportion p if the sample size is n = 500 and the number of successes in the sample is x = 89.

Answer 1

To construct a 99% confidence interval estimate for the population proportion, we can use the formula (p' - EBP, p' + EBP), where p' is the sample proportion and EBP is the margin of error. Plugging in the given values, the confidence interval is approximately 0.129 to 0.227.

Step-by-step explanation:

To construct a confidence interval for a population proportion, we can use the formula: (p' - EBP, p' + EBP), where p' is the sample proportion and EBP is the margin of error. For a 99% confidence interval, the margin of error is approximately 2.58 times the standard error. The standard error can be calculated as the square root of [(p' * q') / n], where q' = 1 - p'. So, plugging in the given values, we have:

p' = 89/500 = 0.178

q' = 1 - p' = 1 - 0.178 = 0.822

Standard error = sqrt[(0.178 * 0.822) / 500] ≈ 0.0189

Margin of error = 2.58 * 0.0189 ≈ 0.0488

Confidence interval = (p' - 0.0488, p' + 0.0488) ≈ (0.129, 0.227)

So, the 99% confidence interval estimate for the population proportion is approximately 0.129 to 0.227.