Solve the problem. for large numbers of degrees of freedom, the critical chi χ squared 2 values can be approximated using the formula chi χ squared 2 equals = one half (x plus startroot 2 x minus 1 endroot )squared 1 2 z+ 2k−12, 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 chi χ squared 2 in a right-tailed hypothesis test with n equals =143 and alpha α equals =0.01.