Assignment
1- A foreign auto manufacturer claims that its sport car (selling for $60,000) gets, on average at least 30 mi./gal. To test this claim, the Consumer Protection Agency hires the G&L Research Lab to evaluate the car's performance. G&L obtain a random sample of 25 sports cars, which are then tested under the optimal conditions specified by the manufacturer. After the test, G&L issue a report stating that the 25 sports cars obtained, on average, 28.9 mi./gal. with a standard deviation of 3.8 mi./gal. Does this report confirm the manufacturer's claim at an alpha (significance level) of 0.05?
2- The local mob wants to buy cement. The cement must have consistent quality, as measured by its variability. The Ace Cement Company claims that the variability of its product, as measured by the standard deviation of the product's strength, is 4 lb/sq. ft. To test this claim, the mob employs a local research lab that owes it a favor. The researchers, in turn, obtain a random sample of Ace's product containing 6 items (i.e., n = 6) and finds its variance to be 16.9 lb./sq. ft. Test at the 5% level whether Ace's claim can be accepted by the mob, or whether the company's owner should start looking for a new place to live.
3- The local mob still wishes to purchase cement. As a result of an unfortunate misunderstanding, the Ace Cement Company (see problem 2) is no longer in business. Therefore, the mob asks the Nock Cement Company and the Out Cement Company to submit bids. Both companies offer their products at identical rock-bottom prices, and both products have equal average strength. Nock, however, claims its product is more reliable because the variability of its strength is less than that of its competitor's product. The mob then decides to make both companies an offer they can't refuse: the mob will take a random sample of 5 bags of cement from each firm, and test Nock's claim. The sample variance of Nock's product is found to be 10.4, while that of Out's product is found to be 14.7. Test Nock's claim at an alpha of 0.05.
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also include a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also Include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.