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