Q8

1. The company that makes JiffyPopper popcorn claims that the average number of calories in a serving of their popcorn is 70 with a standard deviation of 6 calories. A sample of 50 servings of popcorn showed an average of 72 calories. Check the company's claim at α = 0.05.

2. A manufacturer of light bulbs claims that their light bulbs have a mean life of 1150 or more hours with a standard deviation of 80 hours. A random testing of 144 light bulbs had a mean life of 1125 hours. Check the manufacturer's claim. Use a 5% level of significance.

3. A manufacturer claims that their televisions will have an average lifetime of at least 5 years. The standard deviation is 8 months. If 64 sets are selected at random, and their average lifetime was found to be 59 months, would it appear that the manufacturer's claim is correct? Use α = 0.025.

4. The chamber of commerce wants to reduce some of the bus routes in town. They feel that the route going to Park Avenue has an average of less than 30 passengers on board. If that's the case, then it's time to eliminate that route. To help determine what to do, several members of the chamber of commerce rode the route to Park Avenue and observed how many passengers were on the bus. Out of 36 trips on the route, the average number of passengers on the Park Avenue route was 26 with a standard deviation of 5. Using a significance level of 0.025, should the chamber of commerce eliminate the Park Avenue route?

5. A car company claims that the average price of their new car is less than $11,500 with a standard deviation of $700. You feel that their claim is incorrect. You check the price stickers on 32 cars and find the average price is $12,200. At ? = 0.05, test the car company's claim.

6. The manager of Suzi's Diner claims her employees make an average of $9.50 per hour, with a population standard deviation of $0.75. The owner, Pappy, does not believe the claim so he takes a sample of 40 employees and finds their average salary is $9.25. Test the manager's claim at α = 0.03.

7. A pick-up truck dealer claims that his new model will give trouble-free service for at least 15,000 miles. The data below shows a sample of the number of miles of trouble-free service for the dealer's pick-ups that were sold a couple of years ago. Test the dealer's claim at a 2.5% level of significance.

16,000

15,000

14,350

14,500

13,750

13,000

14,250

13,900

8. A quality control inspector at the Yum-Yum Cereal Plant periodically checks the weights of boxes of corn flakes to make sure things are going according to specs. She finds that a sample of 12 boxes weigh-in at at an average of 17.85 ounces with a standard deviation of 0.30 ounces. This sample might suggest that the population average is a little off; like too light. Using a hypothesis test, check to see if, perhaps, the mean weight of all boxes appears to be less than 18 ounces. Use a 1% level of significance.

9. A grocer in Illinois claims that the average grocery bill at his store is $95.00. A sample of the bills of 20 customers had an average of $98.75 with a standard deviation of $7.30. At α = .05, does this evidence support the grocer's claim?

10. A manufacturer makes ball bearings that are supposed to have a mean weight of 30 grams. I'm thinking the actual mean weight is more than 30 grams. I checked 16 ball bearings the other day and found their mean weight to be 31.50 grams with a standard deviation of 4.30 grams. At a 5% level of significance, check to see if the evidence supports my thought.