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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’t 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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Most popular questions from this chapter

Thirty randomly selected seniors at Council High School were asked to report the age (in years) and mileage of their main vehicles. Here is a scatterplot of the data:

(a) What is the equation of the least-squares regression line? Be sure to define any symbols you use.

(b) Interpret the slope of the least-squares line in the context of this problem. (c) One student reported that her 10-year-old car had110000 miles on it. Find the residual for this data value. Show your work

A random sample of 200 New York State voters included 88 Republicans, while a random sample of 300 California voters produced 141 Republicans. Which of the following represents the 95%confidence interval that should be used to estimate the true difference in the proportions of Republicans in New York State and California?

(a) (0.44-0.47)±1.96(0.44)(0.56)+(0.47)(0.53)200+300

(b) (0.44-0.47)±1.96(0.44)(0.56)200+(0.47)(0.53)300

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(e) (0.44-0.47)±1.96(045)(0.55)1200+1300

In an experiment to learn whether Substance M can help restore memory, the brains of 20rats were treated to damage their memories. The rats were trained to run a maze. After a day, 10rats (determined at random) were given M and 7of them succeeded in the maze. Only 2of the 10control rats were successful. The two-sample z test for “no difference” against “a significantly higher proportion of the M group succeeds”

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