Question

You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : μ 1 = μ 2 H a : μ 1 ≠ μ 2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have reason to believe the variances of the two populations are not equal. You obtain a sample of size n 1 = 26 with a mean of M 1 = 89.9 and a standard deviation of S D 1 = 16.2 from the first population. You obtain a sample of size n 2 = 22 with a mean of M 2 = 101.5 and a standard deviation of S D 2 = 6.9 from the second population. The test statistic's value is x ˉ 1 − x ˉ 2 √ S 2 1 n 1 + S 2 2 n 2 =(89.9-101.5)/sqrt(16.2^2/26 + 6.9^2/22) = -3.313. What is the test statistic for this sample? independent samples t-test, df = 34.96 paired samples t-test, df = 34.96 z-test Correct What is the p-value for this sample? use the Welch–Satterthwaite equation) (Report answer accurate to four decimal places.)

p-value =

Answer 1