The statistics department installed energy-efficient lights, heaters, and air conditioners last year. Now they want to determine whether the average monthly energy usage has decreased. Should they perform a one- or two-tailed test? If their previous average monthly energy usage was 3,124 kilowatt hours, what are the null and alternative hypotheses?
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Dr. Ross Darrow believes that nicotine in cigarettes causes cigarette smokers to have higher daytime heart rates on average than do nonsmokers. He also believes that smokers crave the nicotine in cigarettes rather than just smoking for the physical satisfaction of the act and, accordingly, that the average smoker will smoke more cigarettes per day if he or she switches from a brand with a high nicotine content to one with a low level of nicotine. (a) Suppose Ross knows that nonsmokers have an average daytime heart rate of 78 beats per minute. What are the appropriate null and alternative hypotheses for testing his first belief? (b) For the past 3 months, he has been observing a sample of 48 individuals who smoke an average of 15 high-nicotine cigarettes per day. He has just switched them to a brand with a low nicotine content. State null and alternative hypotheses for testing his second belief.
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Hinton Press hypothesizes that the average life of its largest web press is 14,500 hours. They know that the standard deviation of press life is 2,100 hours. From a sample of 25 presses, the company finds a sample mean of 13,000 hours. At a 0.01 significance level, should the company conclude that the average life of the presses is less than the hypothesized 14,500 hours?
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American 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 district was interested in comparing the movie’s popularity in his region with that in all of American’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 district and all of American’s other theaters. (b) At a 1 percent signifi cance level, test these hypotheses.
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Atlas Sporting Goods has implemented a special trade promotion for its propane stove and feels that the promotion should result in a price change for the consumer. Atlas knows that before the promotion began, the average retail price of the stove was $44.95, and the standard deviation was $5.75. Atlas samples 25 of its retailers after the promotion begins and finds the mean price for the stoves is now $42.95. At a 0.02 significance level, does Atlas have reason to believe that the average retail price to the consumer has decreased?
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From 1980 until 1985, the mean price/earnings (P/E) ratio of the approximately 1,800 stocks listed on the New York Stock Exchange was 14.35 and the standard deviation was 9.73. In a sample of 30 randomly chosen NYSE stocks, the mean P/E ratio in 1986 was 11.77. Does this sample present sufficient evidence to conclude (at the 0.05 level of significance) that in 1986,the mean P/E ratio for NYSE stocks had changed from its earlier value?
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Generally Electric has developed a new bulb whose design specifications call for a light out- put of 960 lumens compared to an earlier model that produced only 750 lumens. The com- pany’s data indicate that the standard deviation of light output for this type of bulb is 18.4 lumens. From a sample of 20 new bulbs, the testing committee found an average light output of 954 lumens per bulb. At a 0.05 significance level, can Generally Electric conclude that its new bulb is producing the specifi ed 960 lumen output?
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Maxwell’s Hot Chocolate is concerned about the effect of the recent year-long coffee adver- tising campaign on hot chocolate sales. The average weekly hot chocolate sales two years ago was 984.7 pounds and the standard deviation was 72.6 pounds. Maxwell’s has randomly selected 30 weeks from the past year and found average sales of 912.1 pounds. (a) State appropriate hypotheses for testing whether hot chocolate sales have decreased. (b) At the 2 percent signifi cance level, test these hypotheses.
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The average commission charged by full-service brokerage firms on a sale of common stock is $144, and the standard deviation is $52. Joel Freelander has taken a random sample of 121 trades by his clients and determined that they paid an average commission of $151. At a 0.10 signifi- cance level, can Joel conclude that his clients’ commissions are higher than the industry average?
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Each day, the United States Customs Service has historically intercepted about $28 million in contraband goods being smuggled into the country, with a standard deviation of $16 million per day. On 64 randomly chosen days in 1992, the U.S. Customs Service intercepted an average of $30.3 million in contraband goods. Does this sample indicate (at a 5 percent level of significance) that the Customs Commissioner should be concerned that smuggling has increased above its historic level?
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