Question

6 different baseball players were evaluated against each other based on their number of homeruns hit in 4 different baseball fields. Each player was considered a treatment and each ball field was considered a blocking variable. (alpha = 0.01) There were 24 sample values evaluated. Is there a difference in home runs based on batters? Is there a difference in number of homeruns based on the field played at?

1. State the Null and alternative Hypothesis for the both the Treatment means H0: H1:

2. State the Null and Alternative Hypothesis for the Blocking Means: H0: H1:

3. State the Decision Rule: Use diagram – remember Fcrit &Fcalc

Treatment / Blocking

SS df MS F calc Fcrit Treatments (baseball players) 3304 5 660.8 53.11897 a Blocks (baseball fields) 251.5 3 83.83333 6.739014 b Error 186.6 15 12.44 Total 3742 23

4. Determine Fcrit for the batters and the baseball fields.

5. Based on the results, was there a difference between the batters? The ball fields? Why?

Answer 1

1 H0: There is no significance difference in home runs based on batters
H1: There is atleat 2 batters home runs are different

2.
H0: There is no significance difference in home runs based on field played at
H1: There is atleat 2 filed played at home runs are different

3.Treatment:
Reject H0 for treatment if Test statistic of treatment F_calc > F critical value (i.e. 4.556)
Block :
Reject H0 for Block if Test statistic of Block F_calc > F critical value (i.e. 6.739)

Source	Sum of square	df	mean Square	F	F-critical
Treatment	3304	5	660.8	53.119	4.555614
Block	251.5	3	83.83333333	6.739	5.416965
Error	186.6	15	12.44
Total	3742.1	23

4)

F critical value for treatment = 4.556

F critical value for block = 5.4167

5) Treatment:

Here F value > F critical value so we reject H0

Thus we conclude that There is at least 2 batters home runs are different

Block:

Here F value > F critical value so we reject H0

Thus we conclude that  there is at-least 2 filed played at home runs are different