Read each problem carefully and clearly show all work. Indicate calculator functions used (ie T-Test, 2-SampTTest, etc) as well as calculator entries State your conclusions in terms of the context of the problem.
4) A researcher wants to compare the overall nutrient in children ages 2 to 19 that exclusively use skim milk instead of 1%, 2%, or whole milk. The researcher combined who consumed 1% or 2% milk into a “mixed milk” category. Is there significant evidence to support the belief that at least one mean nutrient intake of children is different from the others at the 10% significance level. The data and the Minitab output is below.
|
Skim Milk |
Mixed Milk |
Whole Milk |
|
860 |
1006 |
880 |
|
850 |
1000 |
935 |
|
870 |
1020 |
845 |
|
900 |
1035 |
818 |
|
920 |
1024 |
870 |
|
886 |
1013 |
875 |
|
855 |
1060 |
881 |
|
860 |
1005 |
836 |
|
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a) Referring again to the problem above, if at least one mean is different, determine which type of milk drinker has a significantly different nutrient intake. Use the Tukey’s Test output below to explain your reasoning. Grouping Information Using the Tukey Method and 95% Confidence Factor N Mean Grouping Mixed 8 1020.38 A Skim 8 875.125 B Whole 8 867.50 B Means that do not share a letter are significantly different.
Test statistic:
F = 78.48
p-value = F.DIST.RT(78.4768, 2, 21) = 0.0000
Decision:
P-value < α, Reject the null hypothesis.
--
Tukey method:
| Group | Sample Mean | Size |
| x̅1 | 875.125 | 8 |
| x̅2 | 1020.375 | 8 |
| x̅3 | 867.5 | 8 |
At α = 0.05, k = 3, N-K = 21, Q value = 3.56
Critical Range, CR = Q*√(MSW/n) = 3.56*√(756.5/8) = 34.62
If |difference| > CR, then the result is significant.
| Comparison | Diff. = (xi - xj) | Critical Range | Results |
| x̅1-x̅2 | -145.25 | 34.62 | Means are different |
| x̅1-x̅3 | 7.625 | 34.62 | Means are not different |
| x̅2-x̅3 | 152.875 | 34.62 | Means are different |
Read each problem carefully and clearly show all work. Indicate calculator functions used (ie T-Test, 2-SampTTest,...
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