Two independent random samples were selected from normally distributed populations with means and variances (1, 21) and (2, 22), respectively The sample sizes, means, and variances are shown in the following table Sample 1 Sample 2 n1 20 n2 15 x1 123 x2 116 12 31 3 22 120 1 a Test H0 12 22 against ...

a H 0 1 2 2 2 H a 1 2 2 2 The test statistic is F Larger sample varianc ...

Two independent random samples were selected from normally distributed populations with means and variances (1, 21) and

Question:

Two independent random samples were selected from normally distributed populations with means and variances (µ1, σ21) and (µ2, σ22), respectively. The sample sizes, means, and variances are shown in the following table:
Sample 1 ... Sample 2
n1 = 20 ..... n2 = 15
x̄1 = 123 .... x̄2 = 116
σ12 = 31.3 .... σ22 = 120.1
a. Test H0: σ12 = σ22 against Ha: σ12 = σ22. Use α = .05.
b. Would you be willing to use a t -test to test the null hypothesis H0: (µ1 - µ2) = 0 against the alternative hypothesis Ha: (µ1 - µ2) = 0? Why?