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CHAPTER 7 Tests of Hypotheses and Significance
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Coefficient of contingency
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7.116. Table 7-35 shows the relationship between hair and eye color of a sample of 200 women. (a) Find the coefficient of contingency without and with Yates correction. (b) Compare the result of (a) with the maximum coefficient of contingency. Table 7-35 HAIR COLOR Blonde EYE COLOR Blue Not Blue 49 30 Not Blonde 25 96
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7.117. Find the coefficient of contingency for the data of (a) Problem 7.109, (b) Problem 7.111 without and with Yates correction. 7.118. Find the coefficient of contingency for the data of Problem 7.114.
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7.119. Two urns, A and B, contain equal numbers of marbles, but the proportions of red and white marbles in each of the urns is unknown. A sample of 50 marbles selected with replacement from each of the urns revealed 32 red marbles from A and 23 red marbles from B. Using a significance level of 0.05, test the hypothesis that (a) the two urns have equal proportions of marbles and (b) A has a greater proportion of red marbles than B. 7.120. Referring to Problem 7.54, find the least number of questions a student must answer correctly before the instructor is sure at a significance level of (a) 0.05, (b) 0.01, (c) 0.001, (d) 0.06 that the student is not merely guessing. Discuss the results. 7.121. A coin that is tossed 8 times comes up heads 7 times. Can we reject the hypothesis that the coin is fair at a significance level of (a) 0.05 (b) 0.10 (c) 0.01 Use a two-tailed test. 7.122. The percentage of A s given in a physics course at a certain university over a long period of time was 10%. During one particular term there were 40 A s in a group of 300 students. Test the significance of this result at a level of (a) 0.05, (b) 0.01. 7.123. Using brand A gasoline, the mean number of miles per gallon traveled by 5 similar automobiles under identical conditions was 22.6 with a standard deviation of 0.48. Using brand B, the mean number was 21.4 with a standard deviation of 0.54. Choosing a significance level of 0.05, investigate whether brand A is really better than brand B in providing more mileage to the gallon. 7.124. In Problem 7.123 is there greater variability in miles per gallon using brand B than there is using brand A Explain.
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7.63. (a) 0.2606. 7.64. (a) Accept the hypothesis if between 22 and 42 red marbles are drawn; reject it otherwise. (b) 0.99. (c) Accept the hypothesis if between 24 and 40 red marbles are drawn; reject it otherwise.
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CHAPTER 7 Tests of Hypotheses and Significance
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7.65. (a) (H0: p 0.5), (H1: p 0.5). (b) One-tailed test. (c) Reject H0 if more than 39 red marbles are drawn, and accept it otherwise (or withhold decision). (d) Reject H0 if more than 41 red marbles are drawn, and accept it otherwise (or withhold decision). 7.66. (a) We cannot reject the hypothesis at a 0.05 level. (b) We can reject the hypothesis at a 0.05 level. 7.67. We cannot reject the hypothesis at a 0.01 level in either (a) or (b). 7.68. We can reject the claim at both levels using a one-tailed test. 7.69. Yes, at both levels, using a one-tailed test in each case. 7.70. The result is significant at a 0.05 level in both a one-tailed and two-tailed test. 7.71. The result is significant at a 0.01 level in a one-tailed test but not in a two-tailed test. 7.72. (a) Yes. (b) No. 7.73. A one-tailed test at both levels of significance shows that brand B is superior to brand A. 7.74. A one-tailed test shows that the difference is significant at a 0.05 level but not a 0.01 level. 7.75. A one-tailed test shows that the new fertilizer is superior at both levels of significance. 7.76. (a) A two-tailed test shows no difference in quality of performance at a 0.05 level. (b) A one-tailed test shows that B is not performing better than A at a 0.05 level. 7.77. A two-tailed test shows that there is no evidence at either level that the mean lifetime has changed. 7.78. A one-tailed test indicates no decrease in the mean at either the 0.05 or 0.01 level. 7.79. A two-tailed test at both levels shows that the product does not meet specifications. 7.80. A one-tailed test at both levels shows that the mean copper content is higher than specifications require. 7.81. A one-tailed test shows that the process should not be introduced if the significance level adopted is 0.01 but should be introduced if the significance level adopted is 0.05. 7.82. Using a two-tailed test at a 0.05 level of significance, we would not conclude that there is a difference in acidity. 7.83. Using a one-tailed test at a 0.05 level of significance, we would conclude that the first group is not superior to the second. 7.84. The apparent increase in variability is not significant at either level.
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