A random sample of 49 statistics examinations was taken.The average score, in the sample, was 84 with a variance of 12.25.The 95% confidence interval for the average examination score of the population of the examinations is
A) 80.48 to 87.52.
B) 77.40 to 86.60.
C) 82.99 to 85.01.
D) 68.00 to 100.00.

Question

Quizplus · Accepted Answer

The confidence interval is calculated using the formula: mean ± (z * (standard deviation/sqrt(n))). Here, the mean is 84, the standard deviation is sqrt(12.25) = 3.5, n = 49, and z for 95% confidence is 1.96. This gives 84 ± (1.96 * (3.5/7)), resulting in the interval 82.99 to 85.01.

A Random Sample of 49 Statistics Examinations Was Taken