BackAge at First Marriage A marriage counselor claims that the median age of women at the time of their first marriage is less than or equal to 27 years old. In a random sample of 65 women, 24 were less than 27 years old, 35 were more than 27 years old, and 6 were 27 years old at the time of their first marriage. At α = 0.05, can you reject the counselor’s claim? (Adapted from U.S. Census Bureau)
Simulating Dice When two dice are rolled, the total is between 2 and 12 inclusive. A student simulates the rolling of two dice by randomly generating numbers between 2 and 12. Does this simulation behave in a way that is similar to actual dice? Why or why not?
According to the National Center for Health Statistics, 22.4% of adults are smokers. A random sample of 300 adults is obtained.
b. In a random sample of 300 adults, what is the probability that at least 50 are smokers?
Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
Health Insurance An insurance agent claims that the median annual amount households with employer health insurance coverage in Hawaii spend on health insurance premiums is at least \$600. In a random sample of 112 such households, 65 households spend less than \$600 and 47 households spend more than \$600. At , can you reject the agent’s claim? (Adapted from The Commonwealth Fund)
In Exercises 9–12, use the sign test for the claim involving nominal data.
Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that there is a difference between the rate of medical malpractice lawsuits that go to trial and the rate of such lawsuits that are dropped or dismissed.
Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
Temperature A meteorologist claims that the median daily high temperature for the month of July in Pittsburgh is Fahrenheit. The high temperatures (in degrees Fahrenheit) for 15 randomly selected July days in Pittsburgh are listed below. At , is there enough evidence to reject the meteorologist’s claim? (Adapted from U.S. National Oceanic and Atmospheric Administration)
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Arsenic in Rice Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.01 significance level to test the claim that the three samples are from populations with the same median.
In Exercises 7–10, (a) state the null and alternative hypotheses and identify which represents the claim.
A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than \$2900.
Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
Attendance An amusement park claims that the mean daily attendance at the park is at least 20,000 people.
In Exercises 1–6, use a sign test to test the claim by doing the following.
a. Identify the claim and state H0 and Ha.
[APPLET] In a study testing the effects of an herbal supplement on blood pressure in men, 11 randomly selected men were given an herbal supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At , can you reject the claim that there was no reduction in diastolic b
How do the requirements for a chi-square test for a variance or standard deviation differ from a z-test or a t-test for a mean?
Statistical Literacy and Critical Thinking
In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.
Number and Proportions
c. For the hypothesis test, identify the value used for the population proportion and use the symbol that represents it.
In Exercises 13 and 14, (c) find the test statistic,
Use
[APPLET] A highway patrol officer stops speeding vehicles on an interstate highway. The genders of the last 25 drivers who were stopped are shown, where F represents a female driver and M represents a male driver. Can you conclude that the stops were not random by gender?
F M M M F M F M F F F M M
F F F M M M F M M F F M
In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.
Good Sample? Given the sequence of data, if we fail to reject randomness, does it follow that the sampling method is suitable for statistical methods? Explain.
Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
e. The value of the test statistic T