Question 3 Samples of 12 members each representing three un

Question 3 - Samples of 12 members, each representing three unions, were tested with respect to their union loyalty. The unions included Autoworkers, Teamsters, and Garment Workers. The union members were also identified by their length of tenure in the union. They were grouped into the categories of Newcomers, Middle-Agers, and Old-Timers. The loyalty test had a potential range of scores from 1 to 100, with 100 reflecting the greatest loyalty. The data observed are shown in the table below. Set the significant level at = .05. (27 points) Autoworkers Teamsters Garment Workers Newcomers 45 55 35 40 60 45 65 55 70 75 60 65 Middle-Agers 40 20 15 25 45 50 35 40 50 40 35 45 Old-Timers 15 10 5 7 20 15 20 15 25 35 30 25

(1) Ho:(Tenure)_______________________________________________ (1 point)

(2) Ho:(Role)_________________________________________________ (1 point)

(3) Ho:(Interaction)_____________________________________________ (1 point)

(4) Appropriate statistical test. (2 points) ______________________________________________________________________

(5) What are the F-statistic, dfs, p-value, and effect size for the interaction effect? (3 points) ______________________________________________________________

(6) What are the F-statistic, dfs, p-value, and effect size for the Tenure main effect? (3 points) ______________________________________________________________

(7) What are the F-statistic, dfs, p-value, and effect size for the Role main effect? (3 points)

(8) Do you need to conduct the follow up test? Why? If yes, report your follow up tests results. (5 points)

(9) What is your decision about null hypothesis? (3 points)

(10) Verbal Conclusions. (5 points)

Solution

1) H0 (Tenure): There is no diffrence among loyalty scores of Newcomers, Middle-Agers, and Old-Timers.

2) H0 (Role): There is no diffrence among loyalty scores of Autoworkers, Teamsters, and Garment Workers.

3) H0 (Interaction): The interaction of tenure and type of role will not draw impact on loyalty scores

4) Two way reparted anova would be approprete for the given problem

The table result is given below

5) F value for interaction = 0.293

P value for F for interaction term = 0.592

effect size for interaction term = 18 / (8363+1890+18+1974)

6)   

F value for tenure = 135.572

P value for F for tenure = 4.83E--13

effect size for tenure = 8363 / (8363+1890+18+1974)

=0.682973

7)

F value for role= 30.646

P value for F for role = 4.18E-06

effect size for Role = 1890 / (8363+1890+18+1974)

8) As p value for role and tenure is less than 5% thus we need to perform follow up test.

9) As p value for role and tenure is less than 5%, thus null hypothesis for tenure and role term can be rejected at 5% level of significance.

10) From the analysis following conclusion can be drawn