Question

The lumen output was determined for each of I = 3 different brands of lightbulbs having the same wattage, with J = 10 bulbs of each brand tested (this is the number of observations in each treatment group). The sums of squares were computed as SSTr = 598.7 and SSE = 4773.1. State the hypotheses of interest (including word definitions of parameters). O u; = true average lumen output for brand / bulbs Ho: M1 = M2 = /3 Ha: at least two u;'s are unequal O u; = true average lumen output for brand / bulbs Ho: M1 # 12 # H3 Ha: at least two uj's are equal O u; = sample average lumen output for brand / bulbs Ho: M1 = M2 = H3 Ha: all three u;'s are unequal O u; = sample average lumen output for brand / bulbs Ho: M1 # 12 # 13 Ha: all three u;'s are equal 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 R to find your p-value using the CDF of the f distribution pf(). Recall the p-value from an F test is always the area to the right of the F test statistic. Example: 1-pf(f test statistic, of1, of2) f statistic = 1.69 (Round your answer to two decimal places.) P-value = x (Round your answer to four places.) State the conclusion in the problem context. O Fail to reject Ho. There are no statistically significant differences in the lumen output. O Reject Ho. There are no statistically significant differences in the lumen output. O Fail to reject Ho. There are statistically significant differences in the lumen output. O Reject Ho. There are statistically significant differences in the lumen output