Show that, for two populations, MSE = s2p, where s2p is the pooled variance defined in Section 10.2 on page 397. Conclude that MSE is

Show that, for two populations, MSE = s2p, where s2p is the pooled variance defined in Section 10.2 on page 397. Conclude that ˆš MSE is the pooled sample standard deviation, sp. Suppose that x is a normally distributed variable on each of two populations and that the population standard deviations are equal. Then, for independent samples of sizes n1 and n2 from the two populations, the variable

Has the t-distribution with df = n1 + n2 ˆ’ 2.

(X1-X2) _ (pe 1-42)