The lumen output was determined for each of k = 3 different brands of lightbulbs having the same wattage, with n, = 9 bulbs of each brand tested (this is the number of observations in each treatment group). The sums of squares were computed as MSTr = 296.000 and MSE = 198.933. State the hypotheses of interest (including word definitions of parameters). O M; = sample average lumen output for brand / bulbs Ho: M1 = M2 = M3 Ha: all three Mi's are unequal O u; = true average lumen output for brand / bulbs Ho: M 1 * 12 * M3 Ha: at least two u 's are equal O M; = sample average lumen output for brand j bulbs Ho: M1 # 12 # 13 Ha: all three u's are equal O M, = true average lumen output for brand / bulbs Ho: M 1 = M2 = M3 Ha: at least two Me's are unequal Use the Single Factor ANOVA F test with (a = 0.05) to decide whether there are any differences in true average lumen outputs among the three brands for this type of bulb. Calculate the F test statistic then use software to find your p-value, Recall the p-value from an F test is always the area to the right of the F test statistic. f statistic = (Round your answer to two decimal places.) P-value = (Round your answer to four places.)