Homework SourseExercise 1303 In a completely randomized design seven experi
{Exercise 13.03}
In a completely randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table (to 2 decimals, if necessary).
What hypotheses are implied in this problem?
0: _________________
a: _________________
At the = .05 level of significance, can we reject the null hypothesis in part (a)?
Calculate the value of the test statistic (to 2 decimals).
______
The p-value is _________________
What is your conclusion?
_________________
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F |
| Treatments | 300 | ______ | ______ | ______ |
| Error | ______ | ______ | ______ | |
| Total | 460 | ______ |
Solution
Sol)
In a completely randomized design, seven experimental units were used for each of the five levels
Hence N=nk =7*5 =35
A) Null hypothesis: All the treatments means are equal
Alternative hypothesis: Alll the treatments means are not equal
level of significance: 5%
Test statistic:
F cal =14.07
Conclusion: F cal=14.07 and F critical value at 5% level with(4,30) =2.69
P value<0.01
F cal > F critical value at 5% level we reject the null hypothesis. Hence the result is significant.
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F |
| Treatments | 300 | (k-1)=4 | 300/4 =75 | 75/5.33 =14.07 |
| Error | 160 | 30 | 160/30=5.33 | |
| Total | 460 | (N-1)=34 |
