Question

I need help Finding the critical value. I know its 12.5916 as answered previously but need to know how exactly to find this answer by hand or on TI-84 Calculator. Thank you for your help.

The answering service for the Health Texas Clinic answers telephone calls after normal working hours for the physicians. It keeps records of telephone calls from patients. A study of 200 evenings resulted in the distribution of number of calls as follows. Test at a 0.05 to determine whether this distribution is Poisson. The parameter A in this case is unknown 1 2 3 4 6 7 8 Number of Calls (x) 5 0 1 2 3 4 6 7 Frequency ( 8 13 30 45 45 25 18 16 You may use the following table to compute the sample mean and the test statistic Si-e) fi-e Р(x) i Xi ei e 5.1208 2.8792 8.2896 1 0 8 0.0256 1.6188 21 13 0.0938 18.7679 33.2682 1.7726 1 13 -5.7679 60 34.3921 0.5609 3 2 30 0.1720 -4.3921 19.2905 4 135 0.2101 42.0157 2.9843 8.9062 3 45 0.2120 5 180 0.1925 38.4969 6.5031 4 45 42.2907 1.0985 125 0.1411 -3.2182 0.3670 6 5 25 28.2182 10.3568 108 0.7634 0.0338 7 6 18 0.0862 17.2366 0.5827 112 7 16 15.7518 0.0039 0.0788 0.2482 0.0616 733 1.0000 Sum 200 5.6676 t

Answer 1

Here we need to perform the $\chi ^{2}$ test for Goodness of fit.

the population is divided into k mutually exclusive classes. Here k=8

the parameter $\lambda$ in this case is unknown hence the statistic follows $\chi ^{2}$ distribution with (k-1-1)=6 degrees of freedom.

THE SUMMATION OF THE LAST COLUMN OF THE TABLE i.e: 5.6676 is the value of our test statistic.

NOW the critical value is found out from the $\chi ^{2}$ table. with degrees of freedom 6 and . which is equal to 12.59.

= 0,05