A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:
A) 77.769
B) 72.231
C) 72.727
D) 77.273
E) 77.145

Question

Quizplus · Accepted Answer

The upper limit of a 95% confidence interval for the population mean is given by the sample mean plus the product of the critical value and the standard error of the mean. The critical value for a 95% confidence interval with 14 degrees of freedom is 2.145. The standard error of the mean is the sample standard deviation divided by the square root of the sample size, which is 25 / sqrt(15) = 5.59. Therefore, the upper limit of the confidence interval is 75 + 2.145 * 5.59 = 77.769.

A Random Sample of Size 15 Taken from a Normally