The lumen output was determined for each of I = 3 different brands of lightbulbs

Question

The lumen output was determined for each of I = 3 different brands of lightbulbs having the same wattage, with J = 8 bulbs of each brand tested. The sums of squares were computed as SSE = 4774.4 and SSTr = 595. State the hypotheses of interest (including word definitions of parameters). mu_1 = sample average lumen output for brand/bulbs H_0: mu_1 = mu_2 = mu_3 H_a: all three mu/s are unequal mu_1 = true average lumen output for brand/bulbs H_0: mu_1 notequalto mu_2 notequalto mu_3 H_a: at least two mu/s are equal mu_1 = sample average lumen output for brand/bulbs H_0: mu_1 notequalto mu_2 notequalto mu_3 H_a: all three mu/s are equal mu_1 = true average lumen output for brand/bulbs H_0: mu_1 = mu_2 = mu_3 H_a: at least two mu/s are unequal Use the F test of ANOVA (alpha = 0.05) to decide whether there are any differences in true average lumen outputs among the three brands for this type of bulb by obtaining as much information as possible about the P-value.

Explanation / Answer

a) Ho: All three means are equal against Ha: At least two means are unequal

b) Given that l=3 and j=8

Therefore N= 24

And also given SSE=4774.4 and SSTr=595

We have MSTr= (SSTr/l-1)=(595/3-1)=297.5

MSE=(SSE/N-l)=(4774.4/24-1)=227.3524

Therefore F-static= (MSTr/MSE) follows F-Distribution with l-1,N-l degrees of freedom

F= (297.5/227.3524)=1.31

Hence F-statistic = 1.31

And the p- value= 0.29

At alpha= 0.05 level p>0.05

Hence we fail to reject Ho.

Therefore there is not enough evidence to alternative hypothesis.

Finally all the three brands are equally effective

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