Probability Exercises
"Probability": Exercises 6.75 and 6.81
6.75The U.S. National Highway Traffic Safety Administration gathers data concerning the causes of highway crashes where at least one fatality has occurred. The following probabilities were determined from the 1998 annual study (BAC is bloodalcohol content). (Source: Statistical Abstract of the United States, 2000, Table 1042.)
6.81Your favorite team is in the final playoffs. You have assigned a probability of 60% that it will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over; your team has lost. What is the probability that it will win the series?
The following exercises are based on the Applications in Medical Screening and Medical Insurance subsection.
"Introduction to Estimation": Exercises 10.11 and 10.14
10.11
a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean.
b. Repeat part (a) with a sample size of 100.
c. Repeat part (a) with a sample size of 400.
d. Describe what happens to the confidence interval estimate when the sample size increases.
10.14
a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that overbar above x is 10. Estimate the population mean with 90% confidence.
b. Repeat part (a) with a sample size of 25.
c. Repeat part (a) with a sample size of 10.
d. Describe what happens to the confidence interval estimate when the sample size decreases.
"Introduction to hypothesis testing": Exercises 11.52 and 11.60
11.52
A statistics practitioner wants to test the following hypotheses with σ = 20 and n = 100:
H sub 0 colon mu equals 100; H sub 1 colon mu is greater than 100 ;
a. Using α = .10 find the probability of a Type II error when μ = 102.
b. Repeat part (a) with α = .02.
c. Describe the effect on β of decreasing α
11.60Suppose that in Example 11.1 we wanted to determine whether there was sufficient evidence to conclude that the new system would not be costeffective. Set up the null and alternative hypotheses and discuss the consequences of Type I and Type II errors. Conduct the test. Is your conclusion the same as the one reached in Example 11.1? Explain.
11.1 It is the responsibility of the federal government to judge the safety and effectiveness of new drugs. There are two possible decisions: approve the drug or disapprove the drug.
"Inference about a population": Exercises 12.73 and 12.74
12.73
a. A statistics practitioner wants to test the following hypotheses:
A random sample of 100 produced . Calculate the pvalue of the test.
b. Repeat part (a) with .
c. Repeat part (a) with.
d. Describe the effect on the zstatistic and its pvalue of decreasing the sample proportion.
12.74Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.
Submit your answers in a 4 to 5page Microsoft Word document and import any associated work in Microsoft Excel.

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Solution: Probability Exercises