Here we use a new example to examine a special estimate of standard error when H
ID: 3150134 • Letter: H
Question
Here we use a new example to examine a special estimate of standard error when H 0 : p 1 = p 2 . We investigate whether there is an increased risk of cancer in dogs that are exposed to the herbicide 2,4-dichlorophenoxyacetic acid (2,4-D). A study in 1994 examined 491 dogs that had developed cancer and 945 dogs as a control group. Of these two groups, researchers identified which dogs had been exposed to 2,4-D in their owner's yard. The results are shown in Table 6.4.
What is the estimate for the standard error? _____
What is the value of the test statistic? _____
Explanation / Answer
a)
Formulating the hypotheses
Ho: p1 - p2 <= 0
Ha: p1 - p2 > 0
Here, we see that pdo = 0 , the hypothesized population proportion difference.
Getting p1^ and p2^,
p1^ = x1/n1 = 0.385858586
p2 = x2/n2 = 0.318809777
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.026636766 [ANSWER, STANDARD ERROR]
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Thus,
z = [p1 - p2 - pdo]/sd = 2.517152782 [ANSWER, TEST STATISTIC]
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