1) The manufacturer of the new subcompact Clipper claims that it will average "40 or more miles per gallon on the open road." Some of the competitors believe this claim is too high. To investigate, an independent testing agency is hired to conduct highway mileage tests. A random sample of 64 clippers showed their mean miles per gallon to be 38.9; with a sample standard deviation of 4.00 miles per gallon. At the 0.01 significance level can the manufacturer's claim be refuted?
2) Last year the records of Ski and Golf, Inc., a sporting goods chain, showed the mean amount spent by a customer was $30. A sample of 40 transactions this month revealed the mean amount spent was $33, with a standard deviation of $12. At the 0.05 significance level can we conclude that the mean amount spent has increased?
3) The county commissioners received a number of complaints from county residents that the Youngsville Fire Department takes longer to respond to fires than the Claredon Fire Department. To check the validity of these claims, a random sample of 60 fires handled by the Youngsville Fire Department was selected. It was found that the mean response time was 6.9 minutes and the standard deviation of the sample was 3.8 minutes. A sample of 70 fires handled by the Claredon Fire Department found the mean response time was 4.9 minutes with a sample standard deviation of 3.0 minutes. At the 0.05 significance level does the data suggest that it takes longer for the Youngsville Department to respond?
4) A recent study was designed to compare smoking habits of young women with those of young men. A random sample of 150 women revealed that 45 of them smoked. A random sample of 100 men indicated that 25 smoked. At the 0.05 significance level does the evidence show that a higher proportion of women smoke?
5) Teledko Associates is a marketing research firm that specializes in comparative shopping. Toledko is hired by General Motors to compare the selling price of the Pontiac Sunbird with the Chevy Cavalier. Posing as a potential customer, a representative of Teledko visited 8 Pontiac dealerships in Metro City and 6 Chevrolet dealerships and obtained quotes on comparable cars. The standard deviation for the selling prices of 8 Pontiac Sunbirds is $350 and on the six Cavaliers, $290. At the 0.01 significance level, is there a difference in the variation in the quotes of the Pontiacs and Chevrolets?
The solution explains how to perform hypothesis tests on five different questions including one on clippers and another for Ski and Golf inc.