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 11.58

23.

Sample 1 Sample 2 Sample 3
Successes 30 60 90
Failures 10 25 50

11.2.23

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

Sample 1 Sample 2 Sample 3 Total
Successes 27.17 57.74 95.09 180
Failures 12.83 27.26 44.91 85
Total 40 85 140 265

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) 2.0468 (c) -value . (d) Since the -value is not , we do not reject . There is insufficient evidence that not all the proportions in are equal.