The lumen output was determined for each of k = 3 different brands of lightbulbs having the same wattage, with n₁ = 9 bulbs of each brand tested (this is the number of observations in each treatment group). The sums of squares were computed as MSTR = 298.450 and MSE = 198.850. State the hypotheses of interest (including word definitions of parameters). O μ₁ = true average lumen output for brand i bulbs ної μ1 #Hz #Из H₂: at least two μ's are equal O μ = sample average lumen output for brand / bulbs Hoi thi = t2 = khô H₂: all three μ's are unequal O μ = true average lumen output for brand i bulbs Ho: H₁ = ₂ = H3 H₂: at least two μ's are unequal O μ = sample average lumen output for brand j bulbs Ho: H₁ H₂ # μ3 H₂: all three μ'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 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.) State the conclusion in the problem context. O Reject Ho. There are no statistically significant differences in the lumen output. O Reject Ho. There are statistically significant differences in the lumen output. O Fail to 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Transcribed Image Text:The lumen output was determined for each of k = 3 different brands of lightbulbs having the same wattage, with nj = 9 bulbs of each brand tested (this is the number of observations in each 298.450 and MSE = 198.850. State the hypotheses of interest (including word definitions of parameters). treatment group). The sums of squares were computed as MSTr O Mj = true average lumen output for brand i bulbs Ho: M₁ M₂ M3 # : at least two μ's are equal sample average lumen output for brand i bulbs Hої М1=M2=M3 Ha: all three μ's are unequal Ha: O μj O Mj = O Mj = true average lumen output for brand i bulbs Но: M1=M2= Мз Ha: at least two μ's are unequal sample average lumen output for brand j bulbs но: M1 #M2+ Мз Ha: all three μ'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 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.) (Round your answer to four places.) p-value = State the conclusion in the problem context. O Reject Ho. There are no statistically significant differences in the lumen output. Reject Ho. There are statistically significant differences in the lumen output. Fail to reject Ho. There are no statistically significant differences in the lumen output. Fail to reject Ho. There are statistically significant differences in the lumen output.

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