An important application of the chi-square distribution is

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21A n important application of the chi-square distribution is a. making inferences about a single population variance b. testing for goodness of fit testing for the independence of two variables d. c. All of these alternatives are correct. 22. The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. n-1 b. k-1 c. number of rows minus 1 times number of columns minus 1 d. a chi-square distribution is not used 23. In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be a. at least 5 b. at least 10 c. no more than 5 d. less than 2 24. A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a a. contingency test b. probability test c. goodness of fit test d. None of these altematives is correct. 25. The degrees of freedom for a contingency table with 12 rows and 12 columns is a. 144 b. 121 d. 120

Answer

Solution-21: Chi-square test can be used to derive inference about a single population variance. It can also be used to test the goodness of fit as well as to test for the independence of two variables. Hence, all the given alternatives are correct. Therefore, option-D is the correct answer. Solution-22: Number of degrees of freedom (Number of rows 1) x (Number of columns 1) Therefore, option-C is the correct answer. Solution-23: Each expected frequency in a goodness of fit test must be at least 5 Therefore, option-A is the correct answer. Solution-24: The test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a goodness of fit test. Therefore, option-C is the correct answer. Solution-25 Degrees of freedom (Number of rows Therefore, option-B is the correct answer. 1) x (Number of columns 1) (12 1) x (12-1) 121

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