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Chapter 10: Q.3.2 (page 619)

To study the long-term effects of preschool programs for poor children, researchers designed an experiment. They recruited 123children who had never attended preschool from low-income families in Michigan. Researchers randomly assigned 62of the children to attend preschool (paid for by the study budget) and the other 61 to serve as a control group who would not go to preschool. One response variable of interest was the need for social services as adults. In the past 10years, 38children in the preschool group and 49in the control group have needed social services.

The Minitab output below gives a 95% con铿乨ence interval for p1-p2. Interpret this interval in context. Then explain what additional information the con铿乨ence interval provides.

Short Answer

Expert verified

From the given information, here, 0does not lie in the computed confidence interval. Thus, it could be said that there is a difference in the two population proportions.

Step by step solution

01

Given Information

It is given in the question that,

02

Explanation

From the overhead output, the 95% confidence interval for the difference in population proportions is (0.0333680,0.347383). It hints that there is a 95% chance that the dissimilarity in population proportion lies between 0.0333680and 0.347383

Here, 0does not lie in the computed confidence interval. Thus, it could be said that there is a difference in the two population proportions.

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Most popular questions from this chapter

DDT in rats Poisoning by the pesticide DDT causes convulsions in humans and other mammals. Researchers seek to understand how convulsions are caused. In a randomized comparative experiment, they compared 6 white rats poisoned with DDT with a control group of 6 unpoisoned rats. Electrical measurements of nerve activity are the main clue to the nature of DDT poisoning. When a nerve is stimulated, its electrical response shows a sharp spike followed by a much smaller second spike. The researchers measured the height of the second spike as a percent of the first spike when a nerve in the rat's leg was stimulated. 78 For the poisoned rats the results were

12.20716.86925.05022.4298.45620.589

The control group data were

11.0749.68612.0649.3518.1826.642

Computer output for a two-sample t-test on these data from software is shown below. (Note that SAS provides two-sided P-values.)

(a) Do these data provide convincing evidence that DDT affects the mean height of the second spike's electrical response? Carry out a significance test to help answer this question.

(b) Interpret the P-value from part (a) in the context

43. Is red wine better than white wine? Observational studies suggest that moderate use of alcohol by adults reduces heart attacks and that red wine may have special benefits. One reason may be that red wine contains polyphenols, substances that do good things to cholesterol in the blood and so may reduce the risk of heart attacks. In an experiment, healthy men were assigned at random to drink half a bottle of either red or white wine each day for two weeks. The level of polyphenols in their blood was measured before and after the two-week period. Here are the percent
changes in level for the subjects in both groups:

(a) A Fathom dotplot of the data is shown below. Use the graph to answer these questions:

  • Are the centers of the two groups similar or different? Explain.
  • Are the spreads of the two groups similar or different? Explain.

(b) Construct and interpret a 90% confidence interval for the difference in mean percent change in polyphenol levels for the red wine and white wine treatments.
(c) Does the interval in part (b) suggest that red wine is more effective than white wine? Explain.

A nuclear power plant releases water into a nearby lake every afternoon at 4:51p.m. Environmental researchers are concerned that fish are being driven away from the area around the plant. They believe that the temperature of the water discharged may be a factor. The scatterplot below shows the temperature of the water (掳C) released by the plant and the measured distance (in meters) from the outflow pipe of the plant to the nearest fish found in the water on eight randomly chosen afternoons.

Computer output from a least-squares regression analysis on these data is shown below.

(a) Write the equation of the least-squares regression line. Define any variables you use.

(b) Interpret the slope of the regression line in context.

(c) A residual plot for the regression is shown on the next page. Is a linear model appropriate for describing the relationship between temperature and distance to the nearest fish? Justify your answer.

(d) Does the linear model in part (a) overpredict or underpredict the measured distance from the outflow pipe to the nearest fish found in the water for a temperature of 29掳? Explain your reasoning.

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

In-line skatersA study of injuries to in-line skaters used data from the National Electronic Injury Surveillance System, which collects data from a random sample of hospital emergency rooms. The researchers interviewed 161 people who came to emergency rooms with injuries from in-line skating. Wrist injuries (mostly fractures) were the most common.6The interviews found that 53people were wearing wrist guards and 6of these had wrist injuries. Of the 108who did not wear wrist guards, 45had wrist injuries.

According to sleep researchers, if you are between the ages of 12and18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours, with a standard deviation of 2.1hours.If we are interested in whether students at this high school are getting too little sleep, which of the following represents the appropriate null and alternative hypotheses?

(a) H0:渭=7.9andHa:渭<7.9

(b) H0:渭=7.9andHa:渭鈮�7.9

(c) H0:渭=9andHa:渭鈮�9

(d)H0:渭=9andHa:渭<9

(e)H0:渭鈮�9andHa:渭鈮�9
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