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Chapter 8: Q136E (page 452)

Volkswagen emissions scandal.Refer to the Significance(December 2015) study on estimating the number of U.S,deaths attributable to nitrogen oxide (NOx) pollutionproduced from illegal VW vehicles, Exercise 2.82 (p. 111).Recall that the researchers computed the estimate foreach of 27 different scenarios involving different valuesof three variables: total distance (in miles) driven by theseillegal VW vehicles, the amount by which the VW vehiclesexceeded the EPA standard for NOx, and the estimated association between NOx emissions and mortality. Summarystatistics for the estimated number of deaths are shown inthe accompanying Minitab printout. Suppose the media

have requested that the researchers provide a single statistic that best represents the center of the distribution of estimated deaths attributable to NOx pollution produced from the illegal VW vehicles. This statistic will be used to publicize the study findings.

a.If you work for Volkswagen and would like to diffuse the media’s reaction to the emissions scandal, which statistic would you choose to report and why?

b.If you support an environmental watch group and would like to incite the media to publicize the emissions scandal, which statistic would you choose to report and why?

Short Answer

Expert verified
  1. The descriptive statistics will be appropriate.

2. The descriptive statistics will be appropriate.

Step by step solution

01

Given information

There are different scenarios involving different values of three variables.

02

For emissions scandal use statistic

We use descriptive statistics in this case. It is helpful to summarize the data to find emissions scandal.

03

Find the category of media to publicize emissions scandal use statistic

We use descriptive statistics in this case also. It is helpful to summarize the data to find emissions scandal.

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Most popular questions from this chapter

Question: Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise 6.29 (p. 348). Recall that the variable of interest was the average distance separating traps—called trap-spacing—deployed by teams of fishermen. The trap-spacing measurements (in meters) for a sample of seven teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap-spacing measurements for eight teams from the Punta Abreojos (PA) fishing cooperative are listed. For this problem, we are interested in comparing the mean trap-spacing measurements of the two fishing cooperatives.

BT Cooperative

93

99

105

94

82

70

86

PA Cooperative

118

94

106

72

90

66

98


Source: Based on G. G. Chester, “Explaining Catch Variation Among Baja California Lobster Fishers Through Spatial Analysis of Trap-Placement Decisions,” Bulletin of Marine Science, Vol. 86, No. 2, April 2010 (Table 1).

a. Identify the target parameter for this study.b. Compute a point estimate of the target parameter.c. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter?d. Find aconfidence interval for the target parameter.e. Use the interval, part d, to make a statement about the difference in mean trap-spacing measurements of the two fishing cooperatives.f. What conditions must be satisfied for the inference, part e, to be valid?

Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study of providing homework assistance to accounting students, Exercise 8.18 (p. 468). Recall that one group of students was given a completed homework solution and another group was given only check figures at various steps of the solution. The researchers wanted to compare the average test score improvement of the two groups. How many students should be sampled in each group to estimate the difference in the averages to within .5 point with 99% confidence? Assume that the standard deviations of the test score improvements for the two groups are approximately equal to 1

Forensic analysis of JFK assassination bullets. Following theassassination of President John F. Kennedy (JFK) in 1963, the House Select Committee on Assassinations (HSCA) conducted an official government investigation. The HSCA concluded that although there was a probable conspiracy involving at least one shooter in addition to Lee Harvey Oswald, the additional shooter missed all limousine occupants. A recent analysis of assassination bullet fragments, reported in the Annals of Applied Statistics(Vol. 1, 2007), contradicted these findings, concluding that the evidence used by the HSCA to rule out a second assassin is fundamentally flawed. It is well documented that at least two different bullets were the source of bullet fragments found after the assassination. Let E= {bullet evidence used by the HSCA}, T= {two bullets used in the assassination}, and= {more than two bullets used in the assassination}. Given the evidence (E), which is more likely to have occurred— two bullets used (T) or more than two bullets used ?

a. The researchers demonstrated that the ratio,P(T\E)/P(Tc\E), is less than 1. Explain why this result supports the theory of more than two bullets used in the assassination of JFK.

b. To obtain the result, part a, the researchers first showed that P(T\E)P(Tc\E)=[PE\T.PT][PE\Tc.PTc]Demonstrate this equality using Bayes’s Rule.

Question: Summer weight-loss camp. Camp Jump Start is an 8-week summer camp for overweight and obese adolescents. Counselors develop a weight-management program for each camper that centers on nutrition education and physical activity. To justify the cost of the camp, counselors must provide empirical evidence that the weight-management program is effective. In a study published in Paediatrics (April 2010), the body mass index (BMI) was measured for each of 76 campers both at the start and end of camp. Summary statistics on BMI measurements are shown in the table.

Source: Based on J. Huelsing, N. Kanafani, J. Mao, and N. H. White, "Camp Jump Start: Effects of a Residential Summer Weight-Loss Camp for Older Children and Adolescents," Pediatrics, Vol. 125, No. 4, April 2010 (Table 3).

a. Give the null and alternative hypotheses for determining whether the mean BMI at the end of camp is less than the mean BMI at the start of camp.

b. How should the data be analyzed, as an independent samples test or as a paired difference test? Explain.

c. Calculate the test statistic using the formula for an independent samples test. (Note: This is not how the test should be conducted.)

d. Calculate the test statistic using the formula for a paired difference test.

e. Compare the test statistics, parts c and d. Which test statistic provides more evidence in support of the alternative hypothesis?

f. The p-value of the test, part d, was reported as p 6 .0001. Interpret this result, assuming a = .01.

g. Do the differences in BMI values need to be normally distributed in order for the inference, part f, to be valid? Explain.

h. Find a 99% confidence interval for the true mean change in BMI for Camp Jump Start campers. Interpret the result.

Independent random samples from normal populations produced the results shown in the next table.

Sample 1


Sample 2

1.23.11.72.83.0

 4.22.73.63.9

a. Calculate the pooled estimate of σ2.

b. Do the data provide sufficient evidence to indicate that μ2>μ1? Test using α=.10.

c. Find a 90% confidence interval for (μ1−μ2).

d. Which of the two inferential procedures, the test of hypothesis in part b or the confidence interval in part c, provides more information about (μ1−μ2)?
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