Problem:1) A recent study of gender preferences among car shoppers found that men and women equally favour economy cars. A marketing analyst doubts these results. He believes that gender differences exist with respect to the purchase of an economy car. He collects data on 400 recent car purchases cross-classified by Gender and Car Type (economy car versus non-economy car). The results are shown in Table At the 10% significance level, determine whether the sample data support the marketing analyst’s claim.
Problem:2) An advertisement for a popular weight loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds.
a.
Set up the competing hypotheses to test the advertisement’s claim.
b.
At the 5% significance level, specify the critical value(s). What is the decision rule?
c.
Calculate the value of the test statistic.
d.
What does the consumer activist conclude?
Problem:3) A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 5 hours. The manufacturer claims that while the new touch phone is more expensive, its battery life is more than twice as long as that of the leading product. In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
a.
Set up the competing hypotheses to test the manufacturer’s claim.
b.
Compute the value of the test statistic.
c.
Use the critical value approach to test the phone manufacturer’s claim at α = 0.05.
Problem:4) A government agency wants to determine whether the average salaries of four various kinds of transportation operators differ. A random sample of five employees in each of the four categories yields the salary data given in the accompanying table.
