Question

10-65. Consider the hypothesis test H0: σ_1^2=σ_2^2 against H1: σ_1^2<σ_2^2. Suppose that the sample sizes are n1 = 6 and n2 = 13, and that s_1^2=23.8 and s_2^2=27.8. Use α = 0.05. Test the hypothesis and explain how the test could be conducted with a confidence interval on σ_1^2/σ_2^2.

Answer 1

The test statistic F = s1^2/s2^2

                              = 23.8/27.8

                              = 0.8561

At alpha = 0.05, the critical value is F(, n1 - 1, n2 - 1) = F(0.95, 5, 12) = 0.2138

Since the test statistic value is not less than the critical value, so we should not reject H₀.

b) At 95% confidence interval , the critical values are F_L = 0.1533

                                                                                    F_R = 3.8911

The 95% confidence interval is

= ( 23.8/27.8) * (1/3.8911) < < ( 23.8/27.8) * (1/0.1533)

= 0.22 < < 5.58

Since the interval contains 1, so we should not reject the null hypothesis.