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Solve the Problem χ2\chi ^ { 2 } Values Can Be Approximated as Follows

question 12

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Solve the problem. For large numbers of degrees of freedom, the critical χ2\chi ^ { 2 } values can be approximated as follows: χ2=12(z+2k1) 2\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 } where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z -value is used, to find the upper critical value, the positive z -value is used. Use this approximation to estimate the critical value of χ2\chi ^ { 2 } in a right-tailed hypothesis test with n=143 and α=0.01\alpha = 0.01


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