Answer:
- There is not a difference between treatment means.
- There is a difference between block means.
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0 : there is no difference between treatment means
H0 : there is no difference between block means
against
Ha: treatment means are not equal.
Ha: block means are not equal.
2) We chose the significance level alpha= 0.01
3) The test statistic to use are
F1= estimated variance from Between hospitals SS/ Estimated Variance from Error SS
F2= estimated variance from Between days SS/ Estimated Variance from Error SS
Which have F distributions with v1=4 and v2= 4 d.f when null hypothesis is true.
Computations:
The necessary computations are shown below.
Assessor Home Zawodny Norman Cingle Holiday Ti Ti2 Sum X2ij
A $54 $52 $48 $45 199 39601 9949
(2916) (2704) (2304) (2025)
B 58 54 5 2 58 222 49284 12348
(3364) (2916) (2704) (3364)
C 43 53 44 54 194 37636 9510
(1849) (2809) (1936) (2916)
D 75 66 63 64 268 71824 18711
(5625) (4356) (3969) (4761)
E 82 85 96 86 349 121801 30561
(6724) (7225) (9216) (7396)
T.j 312 310 303 305 1232 320146 81079
T2.j 97344 96100 91809 93025 378278
Sum X 2 ij 20478 20010 20129 20462 81079
Now Total SS= 81079- (1232)2/ 20
= 81079- 75891.2= 5187.8
Between Treatments SS= 378278/ 5 -75891.2= -235.6
Between Blocks SS= 320146 /4- 75891.2= = 4145.3
Error SS= 5187.8- (-235.6+4145.3)= 1278.1
Source SS df MS F
Treatments -235.6 3 78.533 F1= 0.737
Blocks 4145.3 4 1036.325 F2= 9.73
Error 1278.1 12 106.508
Total 19
For Treatment:
Reject H0 if F> F (0.01) (3,12)=5.95
For blocks:
Reject H0 if F> F (0.01) (4,12)=5.41
Since the computed value F1= 0.737 does not fall in the critical region F> F (0.01) (3,12)= 5.95 and the calculated value F2= 9.73 falls in the region F> F (0.01) (4,12)=5.41 so we conclude:
- There is not a difference between treatment means.
- There is a difference between block means.
