For Problems 6 through 8: An experiment to compare the lifetimes of four differe

Question

For Problems 6 through 8: An experiment to compare the lifetimes of four different brands of spark plugs was carried out. The same number of plugs of each brand was used, and the number of miles until falure was recorded for each plug. Below is an incomplete ANOVA table for analyzing the data. Source df MS p-value 0.0000479 Treatments (Brands) 3 176.482 Error Total 19 235.958 6. What is the replication for each treatment? A. 4 B. 5 C. 16 D. 20 7. Compute the test statistic Fo and the degrees of freedom (dfs) associated with it. A. B. C. Po=15.83, dfs=(4,5) Fo = 3.99, dfsr(3,16) Fo=58.83, dfs=(3,16) D. Fo=15.83, dfss(3,16) what conclusion can you derive from the ANOVA table? Assume = 0.05. A. 8, There are statistically significant differences between the average lifetimes between the brands, and the evidence is very weak. B. There is strong evidence that the linear correlation between brand and lifetime is statistically significant. C. , There are statisticalfy significant differences between the average lifetimes between the brands, and the evidence is very strong. D. The brands do NOT differ with respect to average lifetime, and the evidence is strong

Explanation / Answer

(6) What is replication for each treatment?

solution:

total brand=4

total observation=20(df+1)

therefore, Each brand replicate 20/4 times=5times

answer: option B

(7) Fo and DF associated with it

solution:

MST=SST/DF=58.8273

Error DF=TDF-TR.DF=19-3=16

Error SS=TSS-Tr. SS=235.958-176.482=59.476

MSE=SSE/DF=3.71725

F=MST/MSE=15.8254=15.83

and associated DF(3,16)

therefore,

answer:option D

(8)

pvalue=0.00004

alpha=0.05

pvalue<0.05

We have strong evidence for reject the null hypothesis.

therefore,

answer: option C

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