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Tests involving differences of means and proportions
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7.72. A sample of 100 electric light bulbs produced by manufacturer A showed a mean lifetime of 1190 hours and a standard deviation of 90 hours. A sample of 75 bulbs produced by manufacturer B showed a mean lifetime of 1230 hours with a standard deviation of 120 hours. Is there a difference between the mean lifetimes of the two brands of bulbs at a significance level of (a) 0.05, (b) 0.01
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CHAPTER 7 Tests of Hypotheses and Significance
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7.73. In Problem 7.72 test the hypothesis that the bulbs of manufacturer B are superior to those of manufacturer A using a significance level of (a) 0.05, (b) 0.01. Explain the differences between this and what was asked in Problem 7.72. Do the results contradict those of Problem 7.72 7.74. On an elementary school examination in spelling, the mean grade of 32 boys was 72 with a standard deviation of 8, while the mean grade of 36 girls was 75 with a standard deviation of 6. Test the hypothesis at a (a) 0.05, (b) 0.01 level of significance that the girls are better in spelling than the boys. 7.75. To test the effects of a new fertilizer on wheat production, a tract of land was divided into 60 squares of equal areas, all portions having identical qualities as to soil, exposure to sunlight, etc. The new fertilizer was applied to 30 squares, and the old fertilizer was applied to the remaining squares. The mean number of bushels of wheat harvested per square of land using the new fertilizer was 18.2, with a standard deviation of 0.63 bushels. The corresponding mean and standard deviation for the squares using the old fertilizer were 17.8 and 0.54 bushels, respectively. Using a significance level of (a) 0.05, (b) 0.01, test the hypothesis that the new fertilizer is better than the old one. 7.76. Random samples of 200 bolts manufactured by machine A and 100 bolts manufactured by machine B showed 19 and 5 defective bolts, respectively. Test the hypothesis that (a) the two machines are showing different qualities of performance, (b) machine B is performing better than A. Use a 0.05 level of significance.
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7.77. The mean lifetime of electric light bulbs produced by a company has in the past been 1120 hours with a standard deviation of 125 hours. A sample of 8 electric light bulbs recently chosen from a supply of newly produced bulbs showed a mean lifetime of 1070 hours. Test the hypothesis that the mean lifetime of the bulbs has not changed, using a level of significance of (a) 0.05, (b) 0.01. 7.78. In Problem 7.77 test the hypothesis m significance level of (a) 0.05, (b) 0.01. 1120 hours against the alternative hypothesis m 1120 hours, using a
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7.79. The specifications for the production of a certain alloy call for 23.2% copper. A sample of 10 analyses of the product showed a mean copper content of 23.5% and a standard deviation of 0.24%. Can we conclude at a (a) 0.01, (b) 0.05 significance level that the product meets the required specifications 7.80. In Problem 7.79 test the hypothesis that the mean copper content is higher than in required specifications, using a significance level of (a) 0.01, (b) 0.05. 7.81. An efficiency expert claims that by introducing a new type of machinery into a production process, he can decrease substantially the time required for production. Because of the expense involved in maintenance of the machines, management feels that unless the production time can be decreased by at least 8.0%, they cannot afford to introduce the process. Six resulting experiments show that the time for production is decreased by 8.4% with standard deviation of 0.32%. Using a level of significance of (a) 0.01, (b) 0.05, test the hypothesis that the process should be introduced. 7.82. Two types of chemical solutions, A and B, were tested for their pH (degree of acidity of the solution). Analysis of 6 samples of A showed a mean pH of 7.52 with a standard deviation of 0.024. Analysis of 5 samples of B showed a mean pH of 7.49 with a standard deviation of 0.032. Using a 0.05 significance level, determine whether the two types of solutions have different pH values. 7.83. On an examination in psychology 12 students in one class had a mean grade of 78 with a standard deviation of 6, while 15 students in another class had a mean grade of 74 with a standard deviation of 8. Using a significance level of 0.05, determine whether the first group is superior to the second group.
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