2) (20 pts) The novel A Civil Action (and movie starring John Travolta) is based

Question

2) (20 pts) The novel A Civil Action (and movie starring John Travolta) is based on a case of suspected contamination of municipal wells servicing Woburn, Massachusetts. Shortly after the contaminated wells were discovered, the town was found to have an elevated rate of childhood leukemia. According to one source, there were 16 birth defects out of 414 births when the contaminated wells were being used, and 3 birth defects out of 228 births when the contaminated wells were not being used. (a) (3 pts) Carry out a test of significance to determine whether there is evidence that the rate of birth defects is higher when the polluted wells are in use, being very clear how you have done So. (b) (6 pts) Summarize (with justification) the conclusions you would draw from this study with respect to significance, causation, and generalizability. (c) (3 pts) A 90% confidence interval for the odds ratio is found to be (0.8486903, 16.29630 Write a one-sentence interpretation of this interval. (Don't use the term "odds ratio" in your answer.) (e) (3 pts) Suppose I wanted to test whether the odds of cancer are 10 times higher when the wells are in use than when the wells are not in use. State appropriate null and alternative hypotheses for this question. (f) (3 pts) Based on the confidence interval, will you reject or fail to reject the null hypothesis at the 5% level of significance or cant that be determined? Explain.

Explanation / Answer

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: PContaminated< PNot contaminated
Alternative hypothesis: PContaminated > PNot contaminated

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.0296

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.01398
z = (p1 - p2) / SE

z = 1.82

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 1.82. We use the Normal Distribution Calculator to find P(z > 1.82).

Thus, the P-value = 0.0344.

Interpret results. Since the P-value (0.0344) is less than the significance level (0.05), we have to reject the null hypothesis.

b) We have sufficient evidence in the favor of the claim that there is evidence that the rate of birth defects is higher when the polluted wells are in use.

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