Question

A certain test preparation course is designed to help students improve their scores on the GMAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 3 students' scores on the exam after completing the course: 17,20,26 Using these data, construct a 95% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

95% confidence interval for the average net change is between a lower limit of 11.709 and an upper limit of 30.921.

The critical value that should be used in constructing the confidence interval is 4.303.

Explanation:

Confidence interval is given as mean +/- margin of error (E)

mean = (17+20+26)/3 = 63/3 = 21

sd = sqrt[((17-21)^2 + (20-21)^2 + (26-21)^2) ÷ 3] = sqrt(42÷3) = sqrt(14) = 3.74

n = 3

degree of freedom = n-1 = 3-1 = 2

confidence level (C) = 95% = 0.95

significance level = 1 - C = 1 - 0.95 = 0.05 = 5%

critical value (t) corresponding to 2 degrees of freedom and 5% significance level is 4.303.

The critical value is 4.303

E = t×sd/√n = 4.303×3.74/√3 = 9.291

Lower limit of mean = mean - E = 21 - 9.291 = 11.709

Upper limit of mean = mean + E = 21 + 9.291 = 30.291

95% confidence interval is (11.709, 30.391)