Chapter 14 - Chapter 14 Goodness-of-Fit Tests and...

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275 Chapter 14 Chapter 14 Goodness-of-Fit Tests and Categorical Data Analysis Fill-in-the-Blank Questions Section 14.1 1. A __________ generalizes a binomial experiment by allowing each trial to result in one of k possible outcomes (categories), where k > 2. ANSWER: multinomial experiment 2. The chi-squared distribution has a single parameter ν , called the number __________ of the distribution. ANSWER: degrees of freedom 3. The critical value 2 .05, χ for the chi-squared distribution is the value such that __________ of the area under the 2 curve with degrees of freedom lies to the right of 2 .05, . ANSWER: .05 4. Provided that 5 i np for every i ( i =1, 2, 3, 4, 5), the 2 goodness-of-fit test statistic when category probabilities are completely specified has approximately a chi-squared distribution with __________ degrees of freedom. ANSWER: 4 5. If Z is a standard normal random variable; that is (0,1) ZN :, t h e n 2 Z has a __________ distribution with degrees of freedom = __________. ANSWER: chi-squared, 1
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CHAPTER FOURTEEN 276 6. The area to the right of 4.93 under the 2 degrees of freedom chi-squared curve is __________. ANSWER: .085 Section 14.2 7. One may wish to test 01 1 0 0 : ,...... , versus : kk o a H pp HH == is not true. The null hypothesis is __________ hypothesis in the sense that each 0 i p is a specified number, so that the expected cell counts when 0 H is true are uniquely determined numbers. ANSWER: simple 8. One may wish to test 22 01 2 3 0 : , 2 ( 1) , ( v e r s u s : a H p H H θθ θ = is not true. The null hypothesis is__________ hypothesis because knowing that 0 H is true does not uniquely determine the cell probabilities and expected cell counts but only their general form. ANSWER: composite 9. The 2 χ goodness-of-fit test statistics, when there are 6 categories and 2 parameters to be estimated, has approximately a chi-squared distribution with __________ degrees of freedom. ANSWER: 3 10. If the computed value of the chi-squared test statistic is 2 =2.83, and the test has 2 degrees of freedom, then the null hypothesis 0 H is __________ at .05 level of significance. ANSWER: not rejected 11. It is true that the more the sample correlation coefficient r deviates from __________, the less the normal probability plot resembles a straight line. ANSWER: 1 Section 14.3 12. In a two-way contingency table, if the second row total is 125, the third column total is 60, and the total number of observations is 375, then the estimated expected count in cell (2, 3) is __________. ANSWER: 20 13. A two-way contingency table has 3 rows and 5 columns. Then, the number of degrees of freedom associated with the chi-squared test for homogeneity is __________. ANSWER: 8
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Goodness-of-Fit Tests and Categorical Data Analysis 277 14. The chi-squared test for homogeneity can safely be applied as long as the estimated expected count ˆ ij e is at least __________ for all cells. ANSWER: 5 15. A two-way contingency table has r rows and c columns. Then, the number of degrees of freedom associated with the chi-squared test for independence is __________.
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This note was uploaded on 07/20/2009 for the course MATH 3502 taught by Professor Zahra during the Summer '09 term at Carleton CA.

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Chapter 14 - Chapter 14 Goodness-of-Fit Tests and...

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