Two-Sample Hypothesis Tests
1) Discover Card would like to test the hypothesis that the average credit score for an adult in Dallas is different from the average credit score for an adult in Houston. A random sample of 40 adults in Dallas had an average credit score of 699 and a random sample of 35 adults in Houston had an average credit score of 682. It is believed that the population standard deviation for credit scores is 44 and 41 for Dallas and Houston residents, respectively. Discover Card would like to set? = 0.05. Define Population 1 as Dallas and Population 2 as Houston and use the critical value approach to test this hypothesis.
2) Auto Trader Group (ATG) would like to test the hypothesis that the average age of an imported car on the road is greater than the average age of a domestic car. The following data shows the sample size and the average age of cars for import and domestic cars along with the population standard deviations.
|Sample mean||9.4 years||10.8 years|
|Population standard deviation||3.2 years||2.8 years|
Define Population 1 as import cars and Population 2 as domestic cars. Construct a 90% confidence interval for the difference in population mean and interpret the results.
3) Farmers Insurance Group would like to test the hypothesis that the average number of miles driven per month by a male driver exceeds the average number of miles driven per month by a female driver by more than 50 miles. The following data summarizes the sample statistics for the miles driven per month by each gender. Assume that the population variances are equal.
|Sample standard deviation||130||120|
Define Population 1 as male drivers and Population 2 as female drivers and use the critical value approach to test this hypothesis with? = 0.05.
4) Holiday Inn Express has developed a training program for its hotel staff in an effort to increase customer satisfaction. The employees at the Philadelphia Midtown location completed the training while the employees at the Philadelphia E Penns Landing location did not. Holiday Inn Express would like to test the hypothesis that the average customer satisfaction score at the Midtown location is higher than the average satisfaction score at the E Penns Landing location. The following data summarizes the sample statistics for customer satisfaction, on a scale of 1 to 100, for each location. Assume that the population variances are unequal.
|Midtown||E Penns Landing|
|Sample standard deviation||5.0||6.0|
Define Population 1 as the Midtown location and Population 2 as E Penns Landing location and use the critical value approach to test this hypothesis with? = 0.01.