Question

For a sample of 400 correctional officers at Lucasville State Prison, a researcher believes there is a relationship between “years on the job” and “willingness to help raise money for adult charities.” Using the following data, test the null hypothesis at the .01 level of significance that willingness to help raise donations does not differ by length of service as a correctional officer. In so doing, identify: (1) the research and null hypothesis, (2) the critical value needed to reject the null, (3) the decision that you made upon analyzing the data, and (4) the conclusion you have drawn based on the decision you have made.

                                                                 Years as a Correctional Officer

            Willingness to Help               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

Answer 1

according to the queestion we have to do a chi square test of independence also the cell values are >5 meaning a chi- square test will be the appropriate

(i) The null hypothesis and the alternative hypothesis of the test is given by

H₀: willingness to help raise donation does not differ by length of service as correctional officer(independent)

H₁:willingness to help raise donation differ by length of service as correctional officer( not independent)

the chi-square test statistic is given by

follows distribution with (r-1)(c-1) degrees of freedom where r is the row and c is the coloumn

where

O_i is the observed values of the cell or the observed frequency

and E_i expected value of the cell or the expected frequency

the expected frequency is calculated as

table showing expected frequency

	one	two	three	Four or more
Willing	73.2	73.2	48.8	48.8
Unwilling	46.8	46.8	31.2	31.2

then

(ii) then the critical value of chi square at degrees of freedom 3 at significance level 0.01 is 11.345

(iii)22.250>11.345 hence we reject the null hypothesis

(iv) therefore the willingness to help raise donation differ by length of service as correctional officer