Part 1 : As part of the US. Environmental Protection Agency's (EPA) efforts to "protect human health and safeguard the natural environment," the EPA conducts the Urban Air Toxics Monitoring Program (UATMP). The program has gathered thousands of air samples and analyzed them for concentrations of more than 50 different organic compounds, such as formaldehyde (used as a preservative in vaccinations, to store biological specimens, and in the production of permanent adhesives and insulation). Formaldehyde is also found in the smoke from forest fires, automobile exhaust, and tobacco smoke. The results from UATMP are used to gain insight into the effects of air pollution and determine if efforts to clean up the air are working.

For instance, using air samples from a major city, the EPA can analyze the results and estimate the mean concentration of formaldehyde in the air using a 95% confidence interval. They can then compare the interval with previous years' results to see if there are any trends and if there has been a significant change in the amount of formaldehyde in the air.

You work for the EPA and are asked to interpret the results shown in the graph at the right. The graph shows the point estimate for the population mean concentration and the 95% confidence interval for for formaldehyde over a three-year period. The data are based on air samples taken at one city.

1. Interpreting the Results
   Consider the graph of the mean concentration levels of formaldehyde. For the following years, decide if there has been a change in the mean concentration level of formaldehyde. Explain your reasoning.
   1. From Year 1 to Year 2
   2. From Year 2 to Year 3
   3. From Year 1 to Year 3
2. What Can You Conclude?
   Using the results of Exercise 1, what can you conclude about the efforts to reduce the concentration of formaldehyde in the air?
3. How Do You Think They Did It?

How do you think the EPA constructed the 95% confidence interval for the population mean concentration of the organic compounds in the air? Do the following to answer the question (you do not need to make any calculations).

1. What sampling distribution do you think they used? Why?
2. Do you think they used the population standard deviation in calculating the margin of error? Why or why not? If not, what could they have used?

Part 2 : You work for the company that runs the Powerball lottery. Powerball is a lottery game in which five white balls are chosen from a drum containing 55 balls and one red ball is chosen from a drum containing 42 balls. To win the jackpot, a player must match all five white balls and the red ball. Other winners and their prizes are also shown in the table.

Working in the public relations department, you handle many inquiries from the media and from lottery players. You receive the following e-mail.

" You list the probability of matching only the red ball as 1/69. I know from my statistics class that the probability of winning is the ratio of the number of successful outcomes

to the total number of outcomes. Could you please explain why the probability of matching only the red ball is 1/69? "

Your job is to answer this question, using the probability techniques you have learned in this chapter to justify your answer. In answering the question, assume only one ticket is purchased.

1. How Would You Do It?
   1. How would you investigate the question about the probability of matching, only the red ball?
   2. What statistical methods taught in this chapter would you use?
2. Answering the Question
   Write an explanation that answers the question about the probability of matching only the red ball. Include in your explanation any probability formulas that justify your explanation.
3. Another Question

You receive another question asking how the overall probability of winning a prize in the Powerball lottery is determined. The overall probability of winning a prize in the Powerball lottery is 1/37. Write an explanation that answers the question and include any probability formulas that justify your explanation.

Part 3 : You work for the public relations department of the Social Security Administration. In an effort to design better advertising campaigns, your department decides to conduct a survey to find out the opinions people in the United States have about the Social Security system. One of the questions asked and the results of each response and the respondent's age are shown in the table.

Your department believes that less than 40% of people in the United States expect that Social Security will he able to pay all the benefits they are entitled to under current law. Also, your department believes that the mean age of people in the United States who would say yes to this question is 60 years or older. As the department's research analyst, you must work with the data and determine if these claims can be supported or rejected.

1. How Would You Do It?
   1. What sampling technique would you use to select the sample for the study? Why? What sampling technique would you use if you wanted to select samples from four age groups: 18-34, 35-44, 45-54, and 55 and over?
   2. Which technique in part (a) will give you a sample that is representative of the population?
   3. Identify possible flaws or biases in your study.
2. Testing a Proportion
   Test the claim that less than 40% of people in the United States expect that Social Security will be able to pay all the benefits they are entitled to under current law. Use a = 0.10. Write a paragraph that interprets the test's decision. Does the decision support your department's claim?
3. Testing a Mean
   Test the claim that the mean age of people in the United States who would say yes to the survey question shown in the table is 60 years or older. Use a = 0.10 and assume that the population is normally distributed. Write a paragraph that interprets the test's decision. Is there enough evidence to reject your department's claim?
4. Your Conclusions

On the basis of your analysis of the responses to this survey question, what would you tell your department?

Part 4 : Each year, the National Highway Traffic Safety Administration (NHTSA) together with the National Center for Statistics and Analysis (NCSA) publishes Traffic Safety Facts, which summarizes the motor vehicle traffic crash experience for the United States. Traffic Safety Facts 2005 includes trend data, crash data, vehicle data, and people data. Also, the NHTSA and NCSA publish a report summarizing the motor vehicle crash data of the 32 states in the NHTSA's State Data System.

In 2005, there were 43,443 fatalities in the. United States as a result of motor vehicle crashes. The pie chart at the right shows the national distribution of traffic fatalities with respect to age group. For example, 16% of all motor vehicle fatalities were adults ages 25-34. Using the data from the 32 states in the NHTSA's State Data System as a sample, the contingency table shows the number of motor vehicle fatalities according to age and geographic location within the United States.

Exercises

1. In 2005, how many people in the United. States ages 16-24 died as a result of a motor vehicle crash?
2. Assuming the variables region and age are independent, in. which-region did the number of motor vehicle fatalities for the 16-24 age group exceed the expected number of fatalities?
3. Assuming the variables region and age are independent, in which region did the number of motor vehicle fatalities for the 25-34 age group exceed the expected number of fatalities?
4. At alpha = 0.05, perform a chi-square independence test to determine whether -the variables region and age are independent. What can you conclude?
5. Compare the distribution of the sample of motor vehicle fatalities from the eastern United States the national distribution .What can be concluded
6. Compare the distribution of the sample of motor vehicle fatalities from the central United States the national distribution .What can be concluded
7. Compare the distribution of the sample of motor vehicle fatalities from the western United States the national distribution .What can be concluded
8. In addition to the variables used in this case study what other variables do you think are important considerations when studying, the distribution motor vehicle fatalities?

Price: $49.99

Solution: The downloadable solution consists of 26 pages, 2499 words and 34 charts.
Deliverable: Word Document