STAT 202 Week 3 and 4 Chapter 7,8,9, 10 Assignment

Chapter 7,8,9

One-Sample Hypothesis Tests

Assignment

Please providedetailed solutions to the following problems/exercises (4 problems/exercises x 8 points each):

1) The average number of miles driven on a full tank of gas in a Toyota Corolla before its low-fuel light comes on is 320. Assume this mileage follows the normal distribution with a standard deviation of 30 miles. What is the probability that, before the low-fuel light comes on, the car will travel

a) Less than 330 miles on the next tank of gas?

b) More than 308 miles on the next tank of gas?

c) Between 305 and 325 miles on the next tank of gas?

d) Exactly 340 miles on the next tank of gas?

2) An automotive parts dealer needs an estimate of the mean life he can expect from windshield wiper blades under typical driving conditions. He has already determined that the standard deviation of the population life is 6 months. Suppose we select a simple random sample of 100 wiper blades, collect data on their useful lives, and obtain the following results: n = 100, x- = 21 months, and ¬ = 6 months. Because the dealer uses tens of thousands of these wiper blades annually, he wants to find an interval estimate with a confidence level of 95%.

3) Cinemark Theaters knows that a certain hit movie ran an average of 84 days in each city, and the corresponding standard deviation was 10 days. The manager of the southeastern part of Dallas was interested in comparing the movie’s popularity in his region with that in all of Cinemark’s other theaters. He randomly chose 75 theaters in his region and found that they ran the movie an average of 81.5 days.

a) State appropriate hypotheses for testing whether there was a significant difference in the length of the picture’s run between theaters in the southeastern part of Dallas and all of Cinemark’s other theaters.

b) At a 1% significance level, test these hypotheses.

4) An industrial psychologist has a stress test that is used to determine the amount of stress that managers are under. A value of 80 or higher indicates “high stress.” The industrial psychologist believes that the managers at a large, profitable pharmaceutical firm are not under “high stress” and that the average stress index is less than 80 for managers of the company. A random sample of 50 managers is selected, and their stress index was recorded. Assume that the population standard deviation is 10.15. See the file “Stress Index for Managers”.

a) Test that the data support the industrial psychologist’s belief. Use the general rule of thumb concerning the p value to arrive at a conclusion.

b) What conclusion would you reach if the significance level was .10? .05? .01?                                                                   

  Chapter 10

Two-Sample Hypothesis Tests

Assignment

Please provide detailed solutions to the following problems/exercises (4 problems/exercises x 8 points each):

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 α = 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.

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.

Define Population 1 as male drivers and Population 2 as female drivers and use the critical value approach to test this hypothesis with α = 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.

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 α = 0.01.