A study was conducted to compare the reaction of three different groups of athletes. Specifically, 66 male athletics participated in the study (24 basketball players, 20 soccer players and 22 field hockey players). Each player performed a series of tests to estimate their reaction time. The mean and variance of the reaction time assessment for the three groups of athletes is presented below.

Note, the outcome (X) for this study is reaction time.

ATHLETE
BASKETBALL	24	203.78	147.365
SOCCER	20	195.23	158.219
FIELD HOCKEY	22	204.77	155.271

SOURCE	SUM OF SQUARE	DF	MEAN SQUARE	F
Between
Within (Error)
Total

THE SECOND TABLE IS MEANT TO BE EMPTY UNTIL THE FOLLOWING QUESTIONS ARE ANSWERED

Complete the ANOVA table above by answering the following questions.

1. State the null and alternative hypotheses for the 1-way ANOVA.
2. Calculate the grand mean.Show your work. X_GM=(X)/N = (203.78+195.23+204.77)/(24+20+22)=603.78/66=9.15
3. Calculate the Between-Group Sum of Square. Show your work.
4. Calculate the DF for Between-Group Sum of Square. Show you work.
5. Calculate the Within-Group Sum of Square. Show your work.
6. Calculate the DF for Within-Group Sum of Square. Show your work.
7. Calculate the Between-Group Variance. Show your work.
8. Calculate the Within-Group Variance. Show your work.
9. Calculate the F test Statistics. Show your work.
10. With alpha = 0.05, find the Critical F-value, p-value and state your Conclusion.
11. With alpha = 0.01, find the Critical F-value, p-value and state your Conclusion.

SECTION 2: POST-HOC TEST [14 POINTS]

1. Using alpha = 0.05, find the critic values for Tukey & Scheff tests.
2. How many pairwise comparisons are needed? Show your work.
3. Using the Tukey test, calculate the test statistics foreachpairwise comparison and state your conclusion.Show your work.
4. Using the Scheff test, calculate the test statistics foreachpairwise comparison and state your conclusion.Show your work.