1. The lumen output was determined for each of 3 different brands of 60-watt sof

Question

1. The lumen output was determined for each of 3 different brands of 60-watt soft-white light bulbs, with n 8 of each brand tested. The sums of squares were computed as SSERROR 4773.3 and SSTREATMENT- 591.2 A. State the hypotheses of interest. B. Create the ANOVA table C. Use the F test of ANOVA (which means you can know assumptions were already verified) to decide if there are any differences in true average lumen outputs among the three brands for this type of bulb. LObtain the p-value using the E distribution on your calculator (State hypotheses, test statistic, p-value, decision, and conclusion.)

Explanation / Answer

Ans:

a)

H0:There is no difference in true average lumen outputs among the three brands.

Ha:Atleast one of the brand has different average lumen output than other brands.

b)Number of treatments,k=3

df(treatments)=3-1=2

Total number of subjects,N=3*8=24

df(error)=24-3=21

MS=SS/df

F=MS(treatments)/MS(error)

ANOVA Table:

c)

Test statistic:

F=1.300

p-value=FDIST(1.3,2,21)=0.2935

Assume significance level=0.05

As,p-value>0.05,we fail to reject the null hypothesis.

There is insufficient evidence to conclude that atleast one of the brand has different average lumen output than other brands.

Source SS df MS F Treatments 591.2 2 295.6 1.300 Error 4773.3 21 227.3 Total 5364.5 23

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