Question

The lumen output was determined for each of I = 3 different brands of lightbulbs having the same wattage, with ) = 7 bulbs of each brand tested. The sums of squares were computed as SST = 593.9 and SSE = 4777.5. State the hypotheses of interest (including word definitions of parameters). uj = true average lumen output for brand i bulbs Ho: ui = u2 = 43 Ha: at least two ui's are unequal uj = true average lumen output for brand i bulbs HO: 41 * 42 * 43 Ha: at least two uj's are equal Mi = sample average lumen output for brand i bulbs Ho: u1 = 42 = u3 Ha: all three ui's are unequal Mi = sample average lumen output for brand i bulbs HO: 41 * 42 * 43 Ha: all three ui'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, dfi, df2) f statistic = (Round your answer to two decimal places.) P-value = (Round your answer to four places.) State the conclusion in the problem context. . Fail to reject Ho. There are statistically significant differences in the lumen output. Reject Ho. There are no statistically significant differences in the lumen output. Fail to reject Ho. There are no statistically significant differences in the lumen output. . Reject Ho. There are statistically significant differences in the lumen output.

Answer 1

uj=true average lumen output for brand i bulbs Ho: 1 2= 43 Ha: at least two uis are unequal

f statistic =(MStr/MSE) =(593.9/2)/(4777.5/18)=1.12

p value =0.3480 ( please try 0.3484 if this comes wrong due to rounding of F)

Fail to reject Ho. There are no statistically significant differences in the lumen output.