Problem 4: In an experiment to investigate the performance of 8 different types

Question

Problem 4: In an experiment to investigate the performance of 8 different types of spark plugs intendecd for use on a two-stoke motocycle, 4 plugs of each brand were tested and the number of driving miles(at a constant speed) until plug failure was recorded. A partial ANOVA table for these data follows; Source | df | SS | MSS | F 1000 Brand Error Total 42350 (a) Fill in the missing entries in the ANOVA table. (b) State the null and alternative hypothesis of interest in this experiment. (c) Use a -0.05 to carry out the hypothesis test in part (b)

Explanation / Answer

a)

here df for brands =number of brands-1=k-1=8-1=7

df for error =N-k=8*4-8=24

also as MS=SS/df and F =MS(brand)/MS(error)

from above:

b)

null hypothesis: Ho: all plug brands have equal life time.

alternate hypothesis:Ha: not all plug brands have equal life time.

c)

for 0.05 level and (7,24) degree of freedom ; rejection region F>2.42

as test statsitic 0.679 is not in rejection region we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that not all plug brands have equal life time.

source df SS MSS F Brand 7 7000 1000 0.679 error 24 35350 1472.92 total 31 42350

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