A random sample of 25 statistics examinations was selected. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is _____.
A) 70.02 to 81.98
B) 69.82 to 82.18
C) 70.06 to 81.94
D) 69.29 to 82.71

Question

Quizplus · Accepted Answer

The 99% confidence interval is calculated using the formula: mean ± (z * (standard deviation/sqrt(n))). Here, the mean is 76, the standard deviation is the square root of 144 (which is 12), n is 25, and the z-value for 99% confidence is approximately 2.576. This results in the interval 69.29 to 82.71.

A Random Sample of 25 Statistics Examinations Was Selected