If we wish to accept the null hypothesis 85 percent of the time when it is correct, within how many standard errors around the hypothesized mean should the sample mean fall, in order to be in the acceptance region? What if we want to be 98 percent certain of accepting the null hypothesis when it is true?
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Federal environmental statutes applying to a particular nuclear power plant specify that recy- cled water must, on average, be no warmer than 84°F (28.9°C) before it can be released into the river beside the plant. From 70 samples, the average temperature of recycled water was found to be 86.3°F (30.2°C). If the population standard deviation is 13.5 Fahrenheit (7.5 Celsius) degrees, should the plant be cited for exceeding the limitations of the statute? State and test appropriate hypotheses at α = 0.05.
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State inspectors, investigating charges that a Louisiana soft-drink bottling company underfills its product, have sampled 200 bottles and found the average contents to be 31.7 fluid ounces. The bottles are advertised to contain 32 fluid ounces. The population standard deviation is known to be 1.5 fluid ounces. Should the inspectors conclude, at the 2 percent significance level, that the bottles are being underfilled?
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In 1995, the average 2-week-advance-purchase airfare between Raleigh-Durham, North Carolina, and New York City was $235. The population standard deviation was $68. A1996 survey of 90 randomly chosen travelers between these two cities found that they had paid $218.77, on average, for their tickets. Did the average airfare on this route change significantly between 1995 and 1996? What is the largest α at which you would conclude that the observed average fare is not signifi cantly different from $235?
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Audio Sounds runs a chain of stores selling stereo systems and components. It has been very successful in many university towns, but it has had some failures. Analysis of its failures has led it to adopt a policy of not opening a store unless it can be reasonably certain that more than 15 percent of the students in town own stereo systems costing $1,100 or more. A survey of 300 of the 2,400 students at a small, liberal arts college in the Midwest has discovered that 57 of them own stereo systems costing at least $1,100. If Audio Sounds is willing to run a 5 percent risk of failure, should it open a store in this town?
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The City of Oakley collects a 1.5 percent transfer tax on closed real estate transactions. In an average week, there are usually 32 closed transactions, with a standard deviation of 2.4. At the 0.10 level of significance, would you agree with the tax collector’s conclusion that “sales are off this year” if a sample of 16 weeks had a mean of 28.25 closed sales?
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In 1996, it was estimated that about 72 percent of all U.S. households were cable TV sub- scribers. Newstime magazine’s editors were sure that their readers subscribed to cable TV at a higher rate than the general population and wanted to use this fact to sell advertising space for premium cable channels. To verify this, they sampled 250 of Newstime’s subscribers and found that 194 subscribed to cable TV. At a significance level of 2 percent, do the survey data support the editors’ belief?
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A company, recently criticized for not paying women as much as men working in the same positions, claims that its average salary paid to all employees is $23,500. From a random sample of 29 women in the company, the average salary was calculated to be $23,000. If the population standard deviation is known to be $1,250 for these jobs, determine whether we could reasonably (within 2 standard errors) expect to find $23,000 as the sample mean if, in fact, the company’s claim is true.
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Drive-a-Lemon rents cars that are mechanically sound, but older than those rented by the large national rent-a-car chains. As a result, it advertises that its rates are consider- ably lower than rates of its larger competitors. An industry survey has established that the average total charge per rental at one of the major firms is $77.38. A random sample of 18 completed transactions at Drive-a-Lemon showed an average total charge of $87.61 and a sample standard deviation of’ $19.48. Verify that at a = 0.025, Drive-a-Lemon’s average total charge is significantly higher than that of the major firms. Does this result indicate that Drive-a-Lemon’s rates,’ in fact, are not lower than the rates charged by the major national chains? Explain
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Assuming that the population is approximately normally distributed, is it reasonable to conclude, at a 5 percent significance level, that the average age of the CEOS of all closely held North Carolina corporation is significant greater than 50?
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