An engineer in a local company has conducted an experiment with a single factor,

Question

An engineer in a local company has conducted an experiment with a single factor, hoping to solve a quality problem in one of the company's products. The analysis of the experiment are summarized in the following ANOVA table:

Answer the following questions about the experiment:

1. Determine the values Xi , i = 1,2,3,4,5?
2. If = 0.05, do you conclude that the null hypothesis should be rejected?

3. How many levels of the factor the engineer used in this experiment?

4.How many replicates the engineer used in this experiment?

source DF SS MS F Factor X1 X2 14.18 X3 Error X4 37.75 X5 Total 23 108.63

Explanation / Answer

from above ANOVA table:

1)

2) for test statistic F =29.739 and (5,18) degree of freedom ; p value =0.0000

as p value is less then 0.05 level ;  null hypothesis should be rejected

3) levels of the factor the engineer =df+1 =5+1 =6

4) relicates =24/6=4

source DF SS MS F Factor 70.88/14.18=5 108.63-37.75=70.88 14.18 14.18/0.477=29.739 Error 23-5=18 37.75 37.75/18=0.477 Total 23 108.63

2) for test statistic F =29.739 and (5,18) degree of freedom ; p value =0.0000

as p value is less then 0.05 level ;  null hypothesis should be rejected

3) levels of the factor the engineer =df+1 =5+1 =6

4) relicates =24/6=4

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