Question

Hi, I have a stats question. I couldn't figure it out for a long time. I would appreciate your help.

In an experiment to investigate the performance of four different brands of spark plugs intended for use on a 125-cc motorcycle, five plugs of each brand were tested, and the number of miles (at a constant speed) until failure was observed. A partially completed ANOVA table is given.

Fill in the missing entries, and test the relevant hypotheses using a .05 level of significance. (Give the answer to two decimal places.)

Source of Variation	df	Sum of Squares	Mean Square	F
Treatments
Error		237897.04
Total		319007.87

The data  ---Select--- are are not consistent with the null hypothesis.

You may need to use the appropriate table in Appendix A to answer this question.

Answer 1

from above df(treatment) =k(groups) -1= 5-1 =4

df(Error) =k*(n-1) =5*(5-1)= 20

SS(treatment )=319007.87-237897.04=81110.83

MS(treatment) =SS(treatment )/df =20277.71

MS(error )=SS(error)/df(error )=11894.85

F =MS(treatment)/MS(error )=1.70

Source	df	SS	MS	F
treatments	4	81110.83	20277.71	1.70
error	20	237897.04	11894.85
total	24	319007.87

from excel: for (4,20) df and 0.05 level ; critical value F =finv(0.05,4,20) =2.87

since test statistic <critical value

The data   are consistent with the null hypothesis.