8.2 Testing the Difference Between Means (Small, Independent Samples). Statistics Mrs. Spitz Spring 2009. Objectives/Assignment. How to perform a t-test for the difference between two population means, 1 and 2 using small independent samples. Assignment: pp. 384-388 #1-24 all.
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8.2 Testing the Difference Between Means (Small, Independent Samples)
Assignment: pp. 384-388 #1-24 all
The standard error and the degrees of freedom of the sampling distribution depend on whether or not the population variances and are equal.
Pooled estimate of
And d.f. of n1 + n2 - 2
And d.f. smaller of n1 – 1 or n2 - 1
If the sampling distribution for is a t-distribution, you can use a two-sample t-test to test the difference between two populations 1 and 2.
Ho: 1 = 2 and Ha: 1 2 (Claim)
Because the variances are NOT equal, and the smaller sample size is 10, use the d.f. = 10 – 1 = 9. Because the test is a two-tailed test with d.f. = 9, and = 0.01, the critical values are?
Everybody good so far? Questions?
The graph following shows the location of the critical regions and the standardized test statistic, t.
Ho: 1 2 and Ha: 1 > 2 (Claim)
d.f. = n1 + n2 – 2
= 14 + 16 – 2
Because the test is a right-tailed test, d.f. = 28 and = 0.05, the critical value is 1.701. The rejecetion is t > 1.701.