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CHAPTER 7 Tests of Hypotheses and Significance
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Table 7-28 0 red, 2 white Number of Drawings 6 1 red, 1 white 53 2 red, 0 white 61
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7.105. Two hundred bolts were selected at random from the production of each of 4 machines. The numbers of defective bolts found were 2, 9, 10, 3. Determine whether there is a significant difference between the machines using a significance level of 0.05.
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7.106. (a) Use the chi-square test to determine the goodness of fit of the data of Problem 7.94. (b) Is the fit too good Use a 0.05 level of significance. 7.107. Use the chi-square test to determine the goodness of fit of the data referred to in (a) Problem 7.95, (b) Problem 7.96. Use a level of significance of 0.05 and in each case determine whether the fit is too good. 7.108. Use the chi-square test to determine the goodness of fit of the data referred to in (a) Problem 7.97, (b) Problem 7.98. Is your result in (a) consistent with that of Problem 7.106
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7.109. Table 7-29 shows the result of an experiment to investigate the effect of vaccination of laboratory animals against a particular disease. Using an (a) 0.01, (b) 0.05 significance level, test the hypothesis that there is no difference between the vaccinated and unvaccinated groups, i.e., vaccination and this disease are independent. Table 7-29 Got Disease Vaccinated Not Vaccinated 7.110. Work Problem 7.109 using Yates correction. 7.111. Table 7-30 shows the numbers of students in each of two classes, A and B, who passed and failed an examination given to both groups. Using an (a) 0.05, (b) 0.01 significance level, test the hypothesis that there is no difference between the two classes. Work the problem with and without Yates correction. Table 7-30 Passed Class A Class B 72 64 Failed 17 23 9 17 Did Not Get Disease 42 28
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7.112. Of a group of patients who complained that they did not sleep well, some were given sleeping pills while others were given sugar pills (although they all thought they were getting sleeping pills). They were later asked whether the pills helped them or not. The results of their responses are shown in Table 7-31. Assuming that all patients told the truth, test the hypothesis that there is no difference between sleeping pills and sugar pills at a significance level of 0.05.
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CHAPTER 7 Tests of Hypotheses and Significance
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Table 7-31 Slept Well Took Sleeping Pills Took Sugar Pills 44 81 Did Not Sleep Well 10 35
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7.113. On a particular proposal of national importance, Democrats and Republicans cast votes as indicated in Table 7-32. At a level of significance of (a) 0.01, (b) 0.05, test the hypothesis that there is no difference between the two parties insofar as this proposal is concerned. Table 7-32 In Favor Democrats Republicans 85 118 Opposed 78 61 Undecided 37 25
7.114. Table 7-33 shows the relation between the performances of students in mathematics and physics. Test the hypothesis that performance in physics is independent of performance in mathematics, using (a) 0.05, (b) 0.01 significance level. Table 7-33 MATHEMATICS High Grades PHYSICS High Grades Medium Grades Low Grades 56 47 14 Medium Grades 71 163 42 Low Grades 12 38 85
7.115. The results of a survey made to determine whether the age of a driver 21 years of age or older has any effect on the number of automobile accidents in which he is involved (including all minor accidents) are indicated in Table 7-34. At a level of significance of (a) 0.05, (b) 0.01, test the hypothesis that the number of accidents is independent of the age of the driver. What possible sources of difficulty in sampling techniques, as well as other considerations, could affect your conclusions Table 7-34 AGE OF DRIVER 21 30 NUMBER OF ACCIDENTS 0 1 2 More than 2 748 74 31 9 31 40 821 60 25 10 41 50 786 51 22 6 51 60 720 66 16 5 61 70 672 50 15 7
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