For Exercises 19–22, test whether or not the proportions of successes are the same for all populations.
19.
Sample 1 | Sample 2 | Sample 3 | |
---|---|---|---|
Successes | 10 | 20 | 30 |
Failures | 20 | 45 | 62 |
11.2.19
(a) . : Not all the proportions in are equal.
(b)
Sample 1 | Sample 2 | Sample 3 | Total | |
---|---|---|---|---|
Successes | 9.63 | 20.86 | 29.52 | 60.01 |
Failures | 20.37 | 44.14 | 62.48 | 126.99 |
Total | 30 | 65 | 92 | 187 |
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. (c) 5.991. Reject if . (d) 0.0847 (e) Since is not , we do not reject . There is insufficient evidence that not all the proportions in are equal.