Question

1. The average score of a sample of 100 senior business majors at UTC who took the Graduate Management Admission Test was 530 with a variance of 121. Provide the lower limit of the 99% confidence interval for the mean of the population.

NOTE: WRITE YOUR ANSWER WITH 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN.

Answer 1

Let 'X' be the random variable representing the score obtained by a randomly chosen senior business major at UTC. Then for a sample of 100-

We are given -

Sample size = n = 100

Sample mean =

Sample Variance = S² = 121

Thus, sampling standard error is -

Then the degree of freedom of test statistic = n-1 = 99.

Thus, critical value of test statistic is = t_0.005,99 = 2.626

Then the confidence interval of population mean is -

Thus, the lower confidence bound is -

So, lower bound = 527.1114

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