# ismch14 - 26 Instructor’s Solutions Manual for Statistics...

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Unformatted text preview: 26 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition Chapter 14: Goodness-of-Fit Tests and Contingency Tables 14.1 H : first preferences are evenly distributed across the three books. 1 H : otherwise Book14-1 Made Easy Without Tears Profit&Pleasure Total Observed Number 17 25 18 60 Probability (Ho) 0.333 0.333 0.333 0.999 Expected Number 20 20 20 60 Chi-square calculation 0.45 1.25 0.2 1.9 Chi-square calculation: 2 2 ( ) i i O E Ei χ- = ∑ = 1.90 2 χ (2,.1) = 4.61 Therefore, fail to reject H at the 10% level 14-2 H : Mutual fund performance is equally likely to be in the 5 performance quintiles. 1 H : otherwise Mutual funds14-2 Top 20% 2nd 20% 3rd 20% 4th 20% 5th 20% Total Observed Number 13 20 18 11 13 75 Probability (Ho) 0.2 0.2 0.2 0.2 0.2 1 Expected Number 15 15 15 15 15 75 Chi-square calculation 0.266667 1.666667 0.6 1.066667 0.266667 3.8667 Chi-square calculation: 2 2 ( ) i i O E Ei χ- = ∑ = 3.8667 2 χ (4,.1) = 7.78 Therefore, fail to reject H at the 10% level 14.3 H : Price as a factor in choosing a hospital is equally likely in the three categories 1 H : otherwise Insurance14-3 Not important Important Very important Total Observed Number 142 175 133 450 Probability (Ho) 0.333 0.333 0.333 0.999 Expected Number 150 150 150 450 Chi-square calculation 0.426666667 4.166666667 1.926666667 6.52 Chi-square calculation: 2 2 ( ) i i O E Ei χ- = ∑ = 6.52 2 χ (2,.025) = 7.38 2 χ (2,.05) = 5.9 Therefore, reject H at the 5% level but not the 2.5% level 27 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition 14.4 H : Quality of the output conforms to the usual pattern 1 H : otherwise Electronic component14-4 No faults 1 fault >1 fault Total Observed Number 458 30 12 500 Probability (Ho) 0.93 0.05 0.02 1 Expected Number 465 25 10 500 Chi-square calculation 0.105376344 1 0.4 1.505376 Chi-square calculation: 2 2 ( ) i i O E Ei χ- = ∑ = 1.505 2 χ (2,.05) = 5.99 Therefore, do not reject H at the 5% level 14.5 H : Usual pattern of donations continues 1 H : otherwise Donations14-5 Refusal Request Donation Total Observed Number 65 31 4 100 Probability (Ho) 0.6 0.3 0.1 1 Expected Number 60 30 10 100 Chi-square calculation 0.416666667 0.033333333 3.6 4.05 Chi-square calculation: 2 2 ( ) i i O E Ei χ- = ∑ = 4.05 2 χ (2,.10) = 4.61 Therefore, do not reject H at the 10% level 14.6 H : Student opinion of business courses is the same as that for all courses 1 H : otherwise Opinion14-6 Very useful Somewhat Worthless Total Observed Number 68 18 14 100 Probability (Ho) 0.6 0.2 0.2 1 Expected Number 60 20 20 100 Chi-square calculation 1.066666667 0.2 1.8 3.066667 Chi-square calculation: 2 2 ( ) i i O E Ei χ- = ∑ = 3.067 2 χ (2,.10) = 4.61 Therefore, do not reject H at the 10% level Chapter 14: Goodness-of-Fit Tests and Contingency Tables 28 14.7 H : Customer preferences have not changed from the past 1 H : otherwise Yogurt14-7 A B C D E Total Observed Number 12 16 30 15 7 80 Probability (Ho)...
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ismch14 - 26 Instructor’s Solutions Manual for Statistics...

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