For the following situations, state appropriate null and alternative hypotheses. (a) The Census Bureau wants to determine whether the percentage of homeless people in New York City is the same as the national average. (b) A local hardware store owner wants to determine whether sales of garden supplies are better than usual after a spring promotion. (c) The Weather Channel wants to know whether average annual snowfall in the 1980s was signifi cantly different from the 8-inch average recorded over the past 100 years. (d) A consumer-products investigative magazine wonders whether the fuel efficiency of a new subcompact car is significantly less than the 34 miles per gallon stated on the window sticker.
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Health Electronics, Inc., a manufacturer of pacemaker batteries, specifies that’ the life of each battery is greater than or equal to 28 months. If scheduling for replacement surgery for the batteries is to be based on this claim, explain to the management of this company the conse- quences of Type I and Type II errors.
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A manufacturer of petite women’s sportswear has hypothesized that the average weight of the women buying its clothing is 110 pounds. The company takes two samples of its customers and finds one sample’s estimate of the population mean is 98 pounds, and the other sample pro- duces a mean weight of 122 pounds. In the test of the company’s hypothesis that the population mean is 110 pounds versus the hypothesis that the mean does not equal 110 pounds, is one of these sample values more likely to lead us to accept the null hypothesis? Why or why not?
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Many cities have adopted High Occupancy Vehicle (HOV) lanes to speed commuter traffic to downtown business districts. Planning for Metro Transportation District has depended on a well- established average of 3.4 passengers per HOV. But a summer intern notes that because many firms are sponsoring van pools, the average number of passengers per car is probably higher. The intern takes a sample of 23 vehicles going through the HOV lane of a toil plaza and reports a sample mean of 4.3 passengers, and a standard deviation of 1.5 passengers. At the 0.01 level of significance, does the sample suggest that the mean number of passengers has increased?
In Exercise SC 8-5, what would be the power of the test for μ = 14,000,13,500, and 13,000 if the signifi cance level were changed to 0.10?
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On an average day, about 5 percent of the stocks on the New York Stock Exchange set a new high for the year. On Friday, September 18, 1992, the Dow Jones Industrial Average closed at 3,282 on a robust volume of over 136 million shares traded. A random sample of 120 stocks showed that sixteen had set new annual highs that day. Using a significance level of 0.01, should we conclude that more stocks than usual set new highs on that day?
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In response to criticism concerning lost mail, the U.S. Postal Service initiated new procedures to alleviate this problem. The postmaster general had been assured that this change would reduce losses to below the historic loss rate of 0.3 percent. After the new procedures had been in effect for 2 months, the USPS sponsored an investigation in which a total of 8,000 pieces of mail were mailed from various parts of the country. Eighteen of the test pieces failed to reach their destinations. At a significance level of 0.10, can the post- master general conclude that the new procedures achieved their goal?
What is the probability that we are rejecting a true null hypothesis when we reject the hypoth- esized value because (a) The sample statistic differs from it by more than 2.15 standard errors in either direction? (b) The value of the sample statistic is more than 1.6 standard errors above it? (c) The value of the sample statistic is more than 2.33 standard errors below it?
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Do significantly fewer closed end equity funds sell at a discount than at a premium ? Test at @=0.01
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A finace professor developed a theory that predicted that closed end equity funds should sell at a premium of about 5 percent on average.
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