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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鈥檚 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鈥攃alled trap-spacing鈥攄eployed 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, 鈥淓xplaining Catch Variation Among Baja California Lobster Fishers Through Spatial Analysis of Trap-Placement Decisions,鈥� 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?

Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a children鈥檚 cough remedy, Exercise 8.23 (p. 470). The data (cough improvement scores) for the 33 children in the DM dosage group and the 35 children in the honey dosage group are reproduced in the table below. In Exercise 8.23, you used a comparison of two means to determine whether 鈥渉oney may be a preferable treatment for the cough and sleep difficulty associated with childhood upper respiratory tract infection.鈥� The researchers also want to know if the variability in coughing improvement scores differs for the two groups. Conduct the appropriate analysis, using 伪=0.10

Question: Find the following probabilities for the standard normal random variable z:

a.P(z>1.46)b.P(z<-1.56)c.P(.67鈮�z<2.41)d.P(-1.96鈮�z-.33)e.P(Z鈮�0)f.P(-2.33<z<1.50)

Whistle-blowing among federal employees. Whistle blowing refers to an employee鈥檚 reporting of wrongdoing by co-workers. A survey found that about 5% of employees contacted had reported wrongdoing during the past 12 months. Assume that a sample of 25 employees in one agency are contacted and let x be the number who have observed and reported wrongdoing in the past 12 months. Assume that the probability of whistle-blowing is .05 for any federal employee over the past 12 months.

a. Find the mean and standard deviation of x. Can x be equal to its expected value? Explain.

b. Write the event that at least 5 of the employees are whistle-blowers in terms of x. Find the probability of the event.

c. If 5 of the 25 contacted have been whistle-blowers over the past 12 months, what would you conclude about the applicability of the 5% assumption to this

agency? Use your answer to part b to justify your conclusion.

To compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:

Sample 1

Sample 2

x炉1=5,275蟽1=150

x炉2=5,240蟽2=200

a. Use a 95%confidence interval to estimate the difference between the population means (渭1鈭�渭2). Interpret the confidence interval.

b. Test the null hypothesis H0:(渭1鈭�渭2)=0versus the alternative hypothesis Ha:(渭1鈭�渭2)鈮�0 . Give the significance level of the test and interpret the result.

c. Suppose the test in part b was conducted with the alternative hypothesis Ha:(渭1鈭�渭2)鈮�0 . How would your answer to part b change?

d. Test the null hypothesis H0:(渭1鈭�渭2)=25 versus Ha:(渭1鈭�渭2)鈮�25. Give the significance level and interpret the result. Compare your answer with the test conducted in part b.

e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a鈥揹?
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