Question

A class has been given a statistics exam. In a random sample of 12 students, the test scores are 65, 73, 74, 68, 70, 74, 69, 71, 75 73 67 70, giving us the sample statistics ¯x = 70.75 and s 2 = 9.84. Assume a normal distribution of scores.

(a) Construct a 98% confidence interval for σ 2 .

(b) Construct a 98% confidence interval for σ. (Use your information from Part A, and just state your confidence interval.)

Answer 1

We need to construct the 98% confidence interval for the population variance. We have been provided with the following information about the sample variance and sample size:

s^2 =	9.84
n =	12

The critical values for α=0.02 and df = 11 degrees of freedom are and. The corresponding confidence interval is computed as shown below:

Now that we have the limits for the confidence interval, the limits for the 98% confidence interval for the population standard deviation are obtained by simply taking the squared root of the limits of the confidence interval for the variance, so then: