Question

If X=93, sigma =13, and n=69, construct a 95% confidence interval estimate of the population mean.

a) 91.37 to 94.63
b) 90.12 to 95.88
c) 88.76 to 96.24
d) 92.45 to 93.55

Answer 1

To construct a 95% confidence interval estimate of the population mean, use the formula CI = X ± (Z * (sigma / sqrt(n))). Given X = 93, sigma = 13, and n = 69, the 95% confidence interval estimate is approximately 90.12 to 95.88.

Step-by-step explanation:

To construct a 95% confidence interval estimate of the population mean, we can use the formula for the confidence interval:

CI = X ± (Z * (sigma / sqrt(n)))

Given X = 93, sigma = 13, and n = 69, we substitute these values into the formula:

CI = 93 ± (1.96 * (13 / sqrt(69)))

Calculating the values gives us:

CI ≈ 93 ± 2.35

The 95% confidence interval estimate of the population mean is approximately 90.65 to 95.35, so the correct answer is (b) 90.12 to 95.88.