For Exercises 23–26, test whether or not the proportions of successes are the same for all populations.

  1. State the rejection rule for the p-value method using level of significance , calculate the expected frequencies, and verify that the conditions for performing the test for homogeneity of proportions are met.
  2. Find .
  3. Calculate the p-value.
  4. Compare the p-value with . State the conclusion and the interpretation.

Question 11.60

25.

Sample 1 Sample 2 Sample 3 Sample 4
Successes 10 12 24 32
Failures 6 10 15 30

11.2.25

(a) . : Not all the proportions in are equal. Reject if the -value .

Sample 1 Sample 2 Sample 3 Sample 4 Total
Successes 8.98 12.35 21.88 34.79 78
Failures 7.02 9.65 17.12 27.21 61
Total 16 22 39 62 139

Since none of the expected frequencies is less than 1 and none of the expected frequencies is less than 5, the conditions for performing the test for homogeneity of proportions are met. (b) 1.263 (c) -value .

(d) Since the -value is not , we do not reject . There is insufficient evidence that not all the proportions in are equal.