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?