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Chapter 10: Q.9 (page 622)

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

Shrubs and 铿乺e Fires are a serious threat to shrubs in dry climates. Some shrubs can resprout from their roots after their tops are destroyed. One study of resprouting took place in a dry area of Mexico.7The investigators randomly assigned shrubs to treatment and control groups. They clipped the tops of all the shrubs. They then applied a propane torch to the stumps of the treatment group to simulate a 铿乺e. All 12of the shrubs in the treatment group were resprouted. Only 8 of the 12 shrubs in the control group were resprouted.

Short Answer

Expert verified

From the given information, here, success in the treatment group is 8which is less than 10. It implies that the normality assumption is not fulfilled here.

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

Step by step solution

01

Given Information

It is given in the question that, for treatment group

Number of success (x)=8

Number of events(n)=12

02

Step 2: Explanation

To conduct the two-proportion z -test, the number of successes in both samples must be more than 10. Here, success in the treatment group is 8which is less than 10. It implies that the normality assumption is not fulfilled here.

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

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Most popular questions from this chapter

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.

A large toy company introduces a lot of new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product (as measured by the proportion of customers who had heard of the product by the end of the second month after its introduction). A random sample of 65new products was taken, and a correlation of 0.96was computed. Which of the following is a correct interpretation of this value?

(a) Ninety-six percent of the time, the least-squares regression line accurately predicts first-year sales.

(b) About 92%of the time, the proportion of people who have heard of the product by the end of the second month will correctly predict first-year sales.

(c) About 92%of first-year sales can be explained by the proportion of people who have heard of the product by the end of the second month.

(d) The least-squares regression line relating the proportion of people who have heard of the product by the end of the second month and first-year sales will have a slope of 0.96.

(e) Ninety-two percent of the variation in first-year sales can be explained by the least-squares regression line with proportion of people who have heard of the product by the end of the second month as the explanatory variable.

45. Paying for college College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296students who had summer jobs how much they earned. The financial aid office separated the responses into two groups based on gender. Here are the data in summary form:

(a) How can you tell from the summary statistics that the distribution of earnings in each group is strongly skewed to the right? A graph of the data reveals no outliers. The use of two-sample t procedures is still justified. why?
(b) Construct and interpret a 90%confidence interval for the difference between the mean summer earnings of male and female students at this university.
(c) Interpret the 90%confidence level in the context of this study.

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.

Credit cards and incentives A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following six months.

(a) Is this a problem with comparing means or comparing proportions? Explain.

(b) What type of study design is being used to produce data?
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