1. For a sample of 400 correct
1. For a sample of 400 correctional officers at Lucasville StatePrison, a researcher believes there is a
relationship between “years on the job” and “willingness to helpraise money for adult charities.” Using
the following data, test the null hypothesis at the .05 level ofsignificance that willingness to help raise
donations does not differ by length of service as a correctionalofficer. In so doing, identify: (1) the
research and null hypothesis, (2) the critical value needed toreject the null, (3) the decision that you made
upon analyzing the data, and (4) the conclusion you have drawnbased on the decision you have made.
*Please show all work*
| Willingness to Help | One | Two | Three | Four or More | Total |
| Willing | 60 | 64 | 60 | 60 | 244 |
| Unwilling | 60 | 56 | 20 | 20 | 156 |
| 120 | 120 | 80 | 80 | 400 |
Answer:
Ans:
Chi square test for independence:
H0:There is no association between“years on the job” and “willingness to help raise money for adultcharities.”
Ha:There is association between “years on thejob” and “willingness to help raise money for adult charities.”
degree of freedom=(2-1)*(4-1)=3
critical chi squarevalue=CHIINV(0.05,3)=7.815
Expected count=row sum*column sum/overall sum
| Observed(fo) | |||||
| One | Two | Three | Four or more | Total | |
| Willing | 60 | 64 | 60 | 60 | 244 |
| Unwilling | 60 | 56 | 20 | 20 | 156 |
| Total | 120 | 120 | 80 | 80 | 400 |
| Expected(fe) | |||||
| One | Two | Three | Four or more | Total | |
| Willing | 73.20 | 73.20 | 48.80 | 48.80 | 244 |
| Unwilling | 46.80 | 46.80 | 31.20 | 31.20 | 156 |
| Total | 120 | 120 | 80 | 80 | 400 |
| Chi square=(fo-fe)^2/fe | |||||
| Perfect | Made 4 U | 25 Hours | Total | ||
| Rejected | 2.380 | 1.156 | 2.570 | 2.570 | 8.678 |
| Perfect | 3.723 | 1.809 | 4.021 | 4.021 | 13.573 |
| Total | 6.103 | 2.965 | 6.591 | 6.591 | 22.250 |
Test statistic:
Chi square=22.250
As,test statistic is greater than critical chi square value of7.815,so we reject the null hypothesis.
There is sufficient evidence to conclude that“years on the job” and “willingness to help raise money for adultcharities” are associated.
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