Question

uci a S3 16 CU uellce ierval 1ol the difference in prices between the two stores 3. In a completely randomized design, 7 experimental units were used for each of the three levels of the factor. (2 points each; 6 points total) Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatment Error 432076 5 Total 675643.3 Complete the ANOVA table. b. Find the critical value at the 0.05 level of significance from the F table for testing whether the population means for the three levels of the factors are different. C. Use the critical value approach and a 0.05 to test whether the population means for the three levels of the factors are the same Ps here to search PrSc De Pause

Answer 1

a.

Treatment sum of squares = Total sum of squares - Error sum of squares = 675643.3 - 432076.5 = 243566.8

No. of experimental units = 7  $\Rightarrow$ Total DF = 7-1 = 6

No. of levels of the factor = 3  $\Rightarrow$ Treatment DF = 3-1 = 2

So Error DF = Total DF - Treatment DF = 6-2 = 4

Treatment mean square = (Treatment sum of squares)/(Treatment DF) = 243566.8/2 = 121783.4

Error mean square = (Error sum of squares)/(Error DF) = 432076.5/4 = 108019.125

Calculated F = (Treatment mean square)/(Error mean square) = 121783.4/108019.125 = 1.1274

ANOVA TABLE :-

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Treatment	243566.8	2	121783.4	1.1274
Error	432076.5	4	108019.125
Total	675643.3	6

b.

The F-statistic follows F-distribution with degrees of freedom 2 and 4. Level of significance is 0.05.

Thus critical value for testing whether the population means for the three levels of the factors are different is given by F_0.05;2,4 = 6.94

[ We get the value from the F-distribution table. ]

.

c.

It is seen that calculated F is less than the critical value. So we reject the hypothesis that the population means for the three levels of the factors are different.