Question

7. Perform an appropriate hypothesis test to determine if there is a significant relationship between a student’s race and the punishment received for talking back to teachers in a school district. Interpret the findings.

	In School Suspension	Out of School Suspension	Intermediate Punishment
African-American/Black	19	52	9
Hispanic/Latino	14	39	7
White	9	12	24

Answer 1

Following table shows the row total and column total:

	In school suspension	Out of school suspension	Intermediate punishment	Total
African-American/Black	19	52	9	80
Hispanic/Latino	14	39	7	60
White	9	12	24	45
Total	42	103	40	185

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	In school suspension	Out of school suspension	Intermediate punishment	Total
African-American/Black	18.162	44.541	17.297	80
Hispanic/Latino	13.622	33.405	12.973	60
White	10.216	25.054	9.73	45
Total	42	103	40	185

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
19	18.162	0.038665565
14	13.622	0.010489209
9	10.216	0.144739233
52	44.541	1.249111627
39	33.405	0.937105972
12	25.054	6.801585216
9	17.297	3.979892987
7	12.973	2.750075464
24	9.73	20.9283556
Total		36.84002088

Following is the test statistics:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (3-1)*(3-1)=4

The p-value is: 0.0000

Conclusion: Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that there is a significant relationship between a student’s race and the punishment received for talking back to teachers in a school district.

Excel function used for p-value: "=CHIDIST(36.84, 4)"