Question

A sample of 14 randomly selected students have a sample mean score of 27.6 with a sample standard deviation of 5.1 on a placement test. Construct a 95% confidence interval for the mean score, !, of all students taking the test.

Answer 1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 27.6

S = 5.1

n = 14

df = n – 1 = 13

Confidence level = 95%

Critical t value = 2.1604

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 27.6 ± 2.1604*5.1/sqrt(14)

Confidence interval = 27.6 ± 2.9447

Lower limit = 27.6 - 2.9447 = 24.66

Upper limit = 27.6 + 2.9447 = 30.54

Confidence interval = (24.66, 30.54)