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Chapter 10: Q.7 (page 622)

Explain why the conditions for using two-sample z procedures to perform inference about p1-p2are not met in the settings

Don鈥檛 drink the water! The movie A Civil Action (Touchstone Pictures 1998) tells the story of a major legal battle that took place in the small town of Woburn, Massachusetts. A town well that supplied water to eastern Woburn residents was contaminated by industrial chemicals. During the period that residents drank water from this well, 16of the 414babies born had birth defects. On the west side of Woburn, 3of the 228babies born during the same time period had birth defects.

Short Answer

Expert verified

From the given information, To perform the two proportion z test, the number of successes in both the sample must be more than 10.

Here, success in the second sample is 3 which is less than 10. It implies that the normality assumption is not fulfilled here.

Step by step solution

01

Given Information

It is given in the question that, during the period that residents drank water from this well, 16of the 414babies born had birth defects. On the west side of Woburn, 3of the 228babies born during the same time period had birth defects.

02

Explanation

The values are:

x1=16,n1=414,x2=3,n2=228

To perform the two proportion z test, the number of successes in both the sample must be more than 10.

Here, success in the second sample is 3which is less than 10. It implies that the normality assumption is not fulfilled here.

So, two proportion z-test is not appropriate in this case.

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