Question

Students of two sections of a history course took a common final examination. The course instructor examines the variance in scores between the two sections. He selects random samples of n1 = 11 and n2 = 16 with sample variances of S21=400S12=400 and S22=200S22=200 , respectively. Assuming that the population distributions are normal, construct a 90% confidence interval for the ratio of the population variance.

Multiple Choice

A. [0.90, 2.41]

B. [0.50, 2.00]

C. [0.25, 4.00]

D. [0.79, 5.70]

Answer 1

To construct a 90% confidence interval for the ratio of the population variance, we can use the F-distribution formula.

Step-by-step explanation:

To construct a 90% confidence interval for the ratio of the population variance, we can use the F-distribution. The formula for the confidence interval is:

[(n2 * S21) / (n1 * S22), (n2 * S21) / (n1 * S22)]

Plugging in the given values, we get:

[(16 * 400) / (11 * 200), (16 * 400) / (11 * 200)]

Simplifying this expression, we find: [2.18, 2.18]

Therefore, the 90% confidence interval for the ratio of population variance is [2.18, 2.18].