For Exercises 3–6, perform the indicated Welch's hypothesis test using the critical-value method. The summary statistics were taken from random samples that were drawn independently. For each exercise, follow these steps:

  1. State the hypotheses.
  2. Find the critical value and the rejection rule for this test.
  3. Calculate .
  4. Compare with . State and interpret your conclusion.

Question 10.56

5. Test, at level of significance , whether .

Sample 1
Sample 2

10.2.5

(a) vs. (b) . Reject if . (c) . (d) Since is , we reject . There is evidence at the level of significance that the population mean of Population 1 is less than the population mean of Population 2.