During cooking, doughnuts absorb fat in various amounts. It is believed that the
ID: 3069092 • Letter: D
Question
During cooking, doughnuts absorb fat in various amounts. It is believed that the amount absorbed depends on the type of oil used. For each of four oils (canola, palm, peanut, and soybean), six batches of doughnuts are prepared, and the amount of fat absorbed is measured. The Minitab output follows.
(a) At the significance level of 0.05, can it be concluded that the oil types affect the amount of fat absorbed? Justify your answer with a hypothesis test.
(b) In the present case, is it appropriate to perform the Tukey multiple comparisons test? If yes, summarize the results of the multiple comparisons. If no, explain why.
One-way ANOVA: Fat versus Oil Source DF SS oil Error 20 2018 101 Total 23 3655 MS 3 1637 546 5.41 0.007 S 10.04 R-Sq 44.78% R-Sq (adj ) 36.50% - - Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev +-+-++---- 6 72.00 13.34 6 85.00 7.77 6 76.00 9.88 6 62.00 .22 (---*-) 72 84 96 Pooled StDev-10.04 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of 0il Individual confidence level 98.89% 0il-1 subtracted from: 0il Lower Center Upper+---+ 3-12.24 4.00 20.24 -3.24 13.00 29.24 4-26.24 -10.00 6.24 -40 -20 20 0il-2 subtracted from: 0il Lower Center Upper+---+ 3-25.24 -9.00 .24 4-39.24 -23.00 -6.76 -40 -20 20 0il 3 subtracted from: 0il Lower Center Upper+---+ -30.24 -14.00 2.24 -20 20Explanation / Answer
(a) At the significance level of 0.05, can it be concluded that the oil types affect the amount of fat absorbed? Justify your answer with a hypothesis test.
Ans: The estimated p-value is 0.007. Hence, there at least one oil types have the significant mean doughnuts absorption fat. So, the oil types affect the amount of fat absorbed at 0.05 level of significance.
(b) In the present case, is it appropriate to perform the Tukey multiple comparisons test? If yes, summarize the results of the multiple comparisons. If no, explain why.
Ans: The Tukey multiple comparisons test is needed to find which oil absorb maximum. From the pairwise test, we know that oil 1 has significant fat absorption than oils 2 and 3 at 0.05 level of significance. And oil 2 absorb the maximum among the oils.
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