An existing inventory for a test measuring self-esteem indicates that the scores

Question

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of 11. A psychologist gave the self-esteem test to a random sample of 60 individuals, and their mean score was 60, Construct a 90% confidence interval for the true mean of all test scores. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval? what is the upper limit of the 90% confidence interval?

Explanation / Answer

Solution:
Population standard deviation = 11
Mean = 60
No. of sample = 60
We need to calculate 90% confidence interval as follows:
mean +/- Zalpha/2 * SD/sqrt(n)
so alpha = 0.1 and alpha/2 = 0.05, and Z0.05 = 2.575
60 +/- 2.575*11/sqrt(60)
60+/- 2.575*11/7.746 = 60+/- 3.657
So Confidence interval is 56.3 to 63.4
So Lower limit of the 90% confidence interval is 56.3
and Upper limit of the 90% confidence interval is 63.4

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