Question

Solve the problem. For large numbers of degrees of freedom, the critical values can be approximated using the formula 2x-1 where k is the number of degrees of freedom and z is the crtical vaue. To find the lower critical value, the negative z-value is used,to find the upper critical value, the postive z-value is used. Use this approximation to estimate the critical value of X2 in a two-tailed hypothesis test with n-104 and .10. to find the upper critical value, the positive A. Z2~85.903 and X2~ 122.735 OB. X2#81.186 and X2~128.520 oc. χ2 80.300 and X2 127.406 D. χ2 84.992 and X-21.646

Answer 1

Given: n = 10^4 = > degree of freedom(k) = 103 = n - 1 alpha = 0.10 z_alpha/2 = z_0.05 = 1.645 lower critical value = 1/2(z + squareroot 2k - 1)^2 = 1/2(-1.645 + 2 squareroot (103) - 1)^2 = 80.3001985 upper critical value = 1/2(1.645 + squareroot 2(103) - 1^2 = 127.4058281

Thus, we choose Option C.