Question: 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

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?

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