{Exercise 13.03} In a completely randomized design, seven experimental units wer

Question

{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 ______

Explanation / Answer

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

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