Question

2.In a test of the hypothesis H0: μ = 50 versus Ha: μ < 50, a sample of 40 observations is selected from a normal population and has a mean of 49.0 and a standard deviation of 4.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would reject H0.

3.In a test of the hypothesis H0: μ = 10 versus Ha: μ≠ 10, a sample of 16 observations possessed mean 11.4 and standard deviation 3.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would not reject H0.

Answer 1

2) a) Test statistic

                             

                              = -1.54

P-value = P(Z < -1.54) = 0.0618

b) All level of significance α < 0.0618 will reject H0

3) a) Test statistic

                             

                              = 1.81

P-value = 2 * P(Z > 1.81) = 2 * (1 - P(Z < 1.81)) = 2 * (1 - 0.9649) = 0.0702

b) All level of significance α < 0.0702 will reject H0