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 10.117

5. Test, at level of significance , whether .

Sample 1
Sample 2

10.3.5

(a) ; . Reject if or . (b) 0.7857 (c) 0.65 (d) Since and , we do not reject . There is insufficient evidence that the population proportion from Population 1 is different from the population proportion from Population 2.