Suppose that there are four types of heater (denoted as type 1, type 2, type 3,

Question

Suppose that there are four types of heater (denoted as type 1, type 2, type 3, type 4) and a com- pany wants to assess the durability of these four products before they put them into production. They randomly chose 4 heaters from each product and put them into use. After 60 days, they measured the durability. Now suppose we help them to analyze the data to find out the difference of the durability among these four products.

Source. DF. SS. MS. F

Heater. ? ? 50.8. ?

Error. ? ? ? X

Total. ? 319.9. X. X

(a). Identify the response, Factor(s) and all Treatments. Is this a balanced design? Why?

(b). Complete ANOVA table above by finding out the values in the question marks (show work).

(c). With an alpha level .05, see if there is sufficient evidence to indicate that at least two kinds of heaters are different. Clearly state all five steps.

(d). If you want to compare all pair of means, which procedure will you use (Tukey, Bonferroni or Scheff)? Why?

Explanation / Answer

Ans:

n=4*4=16

Mean square between the groups=SS/(k-1)

k=4

SS=50.8*3=152.4

Mean square within the groups=SS/(n-k)

n-k=16-4=12

Total SS=SSbetween +SSwithin

SSwithin=319.9-152.4=167.5

F=MSbetween/MSwithin=50.8/13.96=3.64

p-value==FDIST(3.64,3,12)=0.0448

As,p-value=0.0448<0.05,we reject null hypothesis.

There is sufficient evidence to conclude that at least two kinds of heaters are different.

df SS MS F Heater(between) 3 152.4 50.8 3.64 Error(within) 12 167.5 13.96 Total 15 319.9

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