The lumen output was determined for each of 1 = 3 different brands of lightbulbs

Question

The lumen output was determined for each of 1 = 3 different brands of lightbulbs having the same wattage, with State the hypotheses of interest (including word definitions of parameters) = 7 bulbs of each brand tested. The sums of squares were computed as SSE = 4778 and SSTr = 595.8 , true average lumen output for brand i bulbs at least two 's are unequal .-sample average lumen output for brand i bulbs Hai all three 's are unequal ' = true average lumen output for brand i bulbs : at least two 's are equal .-sample average lumen output for brand i bulbs Hai all three 's are equal Use the F test of ANOVA (a0.05) 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. (Round your answer to two decimal places.) What can be said about the P-value for the test? P-value > 0.100 0.050 P-value

Explanation / Answer

Hypotheses are as per option A
H0: mu1 = mu2 = mu3
Ha: at least two mu(i) are unequal

SSE = 4778
SST = 595.8
c = 3 (number of columns in data table)
N = 7*3 = 21 (total number of observations)

MSTR = SST/(c-1) = 595.8/(3-1) = 297.9

MSE = SSE/(N-c) = 4778/18 = 265.4444

F = MSTR/MSE = 297.9/265.4444 = 1.1223

p-value = 0.3473 (using standard F table)

p-value > 0.1

As p-value is greater than the significance level of 0.1, fail to reject H0. Option A

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