Statistics with chi square

Question

Race of Offenders

Type of Lawyer. White    Nonwhite.   Total

Private.                 95.        25.         120
                          (47.5%). (8.3%)
Court appointed  105.         275.      380
                             (52.5%). (91.7%)
Total.                   . 200.       300.       500

Instructions: Analyze the following table. Use the observed frequencies in the table to calculate chi square. . Show your findings in a table with chi square (Chi square = 100.9 with 1 degree of freedom).

Answer 1

You have 4 cells with frequescise in your problem - 

95 , 25, 105 , 275 

best way to do this problem is make  2X2 table and put observed and expected frequencies in the table. 

as explained above to calculate expected frequency you will take row total & column total & devide by grand total for each cell.

so for 95 - Exp freq = (120*200/500) = 48

for     25 - Exp freq = ( 120*300/500) = 72

for    105 Exp Freq  = ( 380*200/500) =  152 

for    275   Exp Freq = ( 275*300/500) = 228

 

Now calculate this for each cell  (Observed - Expected) ^2/ Expected and add them - 

( 95-48)^2/48 + (25-72)^2/72 + ( 105-152)^2/152  + ( 275-228)^2/ 228 = 46.02 + 30.68 + 14.53 + 0.69 = 100.9

degrees of freedom = (# of rows -1 ) ( # of columns-1) = ( 2-1)(2-1) = 1 

let me know if you have any questions or you don't understand anything. 

 

 

 

 

Answer 2

Chi squared=(observed frequency - expected frequency) squared, divided by expected frequency. 

Here, chi squared = 100.9, and you would use that as the sum of each variable's chi square. Each number in your table is an observed frequency. For instance 25 non white persons with private lawyers would be one observed frequency.

 

Your problem is incomplete because in order to calculate the total chi square, you would need the observed and expected frequencies for all four probabilities.

How to calculate expected frequencies? Here, 300 of 500 are not white. If the null were true, that number would equal the proportion of non whites (300/500) multiplied by the number of people with private lawyers, so that (300/500) * 120 or 0.6 * 120 or 72. So 72 would be the expected frequency for non whites with private lawyers. 25 is the observed frequency. Thus (25 - 72) squared divided by 72. That is 30.68, which is the chi square value for non whites with private lawyers.