Jeff Richardson, the receiving clerk for a chemical-products distributor, is faced with the continuing problem of broken glassware, including test-tubes, petri dishes, and fl asks. Jeff has determined some additional shipping precautions that can be undertaken to prevent breakage, and he has asked the Purchasing Director to inform the suppliers of the new measures. Data for 8 suppliers are given below in terms of average number of broken items per shipment. Do the data indicate, at α = 0.05, that the new measures have lowered the average number of broken items?
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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Additives-R-Us has developed an additive to improve fuel effi ciency for trucks that pull very heavy loads. They tested the additive by randomly selecting 18 trucks and dividing them into 9 pairs. In each pair, both trucks hauled the same type of load over the same roadway, but only one truck used fuel with the new additive. Different pairs followed different routes and carried different loads. The resulting fuel effi ciencies (in miles per gallon) are given below. Do the data indicate, at α = 0.01, that trucks using fuel with the additive achieved signifi cantly better fuel effi ciency than trucks using regular fuel?
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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Aquarius Health Club has been advertising a rigorous program for body conditioning. The club claims that after 1 month in the program, the average participant should be able to do eight more push-ups in 2 minutes than he or she could do at the start. Does the random sample of 10 program participants given below support the club’s claim? Use the 0.025 level of signifi cance.
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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Donna Rose is a production supervisor on the disk-drive assembly line at Winchester Technologies. Winchester recently subscribed to an easy listening music service at its factory, hoping that this would relax the workers and lead to greater productivity. Donna is skeptical about this hypothesis and fears the music will be distracting, leading to lower productivity. She sampled weekly production for the same six workers before the music was installed and after it was installed. Her data are given below. At α = 0.02, has the average production changed at all?
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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Modems transmit information across telephone lines from one computer to another. Their speed is rated in baud, the number of bits per second that they can transmit. Because of several technical factors, actual transmission rate varies from fi le to fi le. Anne Evans was shopping for a new 28,800 baud modem. In testing two modems to decide which to purchase, she transmitted 7 randomly chosen fi les with both modems and recorded the following rates (in thousands of baud).
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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A large hotel chain is trying to decide whether to convert more of its rooms to nonsmoking rooms. In a random sample of 400 guests last year, 166 had requested nonsmoking rooms. This year, 205 guests in a sample of 380 preferred the nonsmoking rooms. Would you recommend that the hotel chain convert more rooms to nonsmoking? Support your recommendation by testing the appropriate hypotheses at a 0.01 level of signifi cance.
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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Two different areas of a large eastern city are being considered as sites for day-care centers. Of 200 households surveyed in one section, the proportion in which the mother worked fulltime was 0.52. In another section, 40 percent of the 150 households surveyed had mothers working at full-time jobs. At the 0.04 level of signifi cance, is there a signifi cant difference in the proportions of working mothers in the two areas of the city?
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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On Friday, 11 stocks in a rand om sample of 40 of the roughly 2,500 stocks traded on the New York Stock Exchange advanced; that is, their price of their shares increased. In a sample of 60 NYSE stocks taken on Thursday, 24 advanced. At α = 0.10, can you conclude that a smaller proportion of NYSE stocks advanced on Friday than did on rsday?
- Find the mean change in earnings per share between 1991 and 1992.
- Find the standard deviation of the change and the standard error of the mean.
- Were average earnings per share different in 1991 and 1992? Test at α = 0.02.
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MacroSwift has recently released a new word-processing product, and they are interested in determining whether people in the 30–39 age group rate the program any differently than members of the 40–49 age group. MacroSwift randomly sampled 175 people in the 30–39 age group who purchased the product and found 87 people who rated the program as excellent, with 52 people who would purchase an upgrade. They also sampled 220 people in the 40–49 age group and found 94 people who gave an excellent rating, with 37 people who plan to purchase an upgrade. Is there any signifi cant difference in the proportions of people in the two age groups who rate the program as excellent at the α = 0.05 level? Is the same result true for proportions of people who plan to purchase an upgrade?
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A coal-fi red power plant is considering two different systems for pollution abatement. The fi rst system has reduced the emission of pollutants to acceptable levels 68 percent of the time, as determined from 200 air samples. The second, more expensive system has reduced the emission of pollutants to acceptable levels 76 percent of the time, as determined from 250 air samples. If the expensive system is signifi cantly more effective than the inexpensive system in reducing pollutants to acceptable levels, then the management of the power plant will install the expensive system. Which system will be installed if management uses a signifi cance level of 0.02 in making its decision?
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