Let the test statistic T have a t distribution when H0 is true. Give the significance level for each of the following situations: A. Ha: mu > m0, df = 15, rejection region t > 3.733
B. Ha : mu < mu 0 n = 24, rejection region t < - 2.500
C. Ha: mu not= mu 0 n = 31, rejection region t >1.697 or t < - 1.697

Step-by-step explanation:

a) This is a right tailed test. The significance level is α. The critical value corresponding to 1 - α is 3.733. From the t distribution table with a df of 15, 1 - α = 0.999

α = 1 - 0.999 = 0.001

b) This is a left tailed test. Degree of freedom, df = n - 1 = 24 - 1 = 23

The critical value corresponding to 1 - α is - 2.500. From the t distribution table with a df of 23, 1 - α = 0.99

α = 1 - 0.99 = 0.01

c) This is a two tailed test. Degree of freedom, df = n - 1 = 31 - 1 = 30

The critical value corresponding to 1 - α/2 is 1.697. From the t distribution table with a df of 30, 1 - α/2 = 0.95

α/2 = 1 - 0.95 = 0.05

α = 2 × 0.05

α = 0.1

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