Refer to Exercises 7.20 and 7.21. The pooled estimator of the common variance 2 is given

Refer to Exercises 7.20 and 7.21. The pooled estimator of the common variance σ² is given by

Show that

has a Student’s T distribution with (n₁ + n₂ - 2) df. Recall that T = Z/√x²/v has a Student’s T distribution with v df and use the results of Exercises 7.20c and 7.21.

Data from Exercise 7.20

Let (y̅₁, s₁²) and (y̅₂ , s₂²) be the means and variances of two independent random samples of sizes n₁ and n₂, respectively, selected from normal populations with different means, μ₁ and μ₂, but with a common variance, σ².

Transcribed Image Text:

(n- 1)s + (n2 - 1)s3 n + n2 - 2 ||