Question

13. Given the following information, determine the confidence interval.

n = 49; x = 405; s = 21; CL = 99.7%

Answer choices:
(402, 408)
(401, 409)
(399,411)
(396, 414)

Answer 1

The formula for calculating a confidence interval for the mean is:

CI = X ± Zα/2 * (s/√n)

where X is the sample mean, s is the sample standard deviation, n is the sample size, and Zα/2 is the z-score for the desired confidence level.

In this case, n = 49, x = 405, s = 21, and CL = 99.7%. The corresponding z-score for a 99.7% confidence level is 2.967.

Plugging in the values, we get:

CI = 405 ± 2.967 * (21/√49)

CI = 405 ± 9.67

CI = (395.33, 414.67)

Therefore, the confidence interval is (396, 414). Answer choice (D) is the correct one.