The summary statistics in Exercises 5–7 and 9–11 were taken from random samples that were drawn independently. Let and denote the size of samples 1 and 2, respectively. Let and denote the number of successes in samples 1 and 2, respectively.

For Exercises 5–7, perform the indicated hypothesis test using the critical-value method. Answer (a)–(d) for each exercise.

  1. State the hypotheses and find the critical value and the rejection rule.
  2. Calculate .
  3. Calculate .
  4. Compare with . State and interpret your conclusion.

Question 10.119

7. Test, at level of significance , whether .

Sample 1
Sample 2

10.3.7

(a) . . Reject if (b) . (c) . (d) Since is ≥ 2.33, we reject . There is evidence at the level of significance that the population proportion of Population 1 is greater than the population proportion of Population 2.