Does bread lose its vitamins when stored? Small loaves of bread were prepared wi
ID: 3375721 • Letter: D
Question
Does bread lose its vitamins when stored? Small loaves of bread were prepared with flour that was fortified with a fixed amount of vitamins. After baking, the vitamin C content of two loaves was measured. Another two loaves were baked at the same time, stored for one day, and then the vitamin C content was measured. In a similar manner, two loaves were stored for three, five and seven days before measurements were taken. The units are milligrams per hundred grams of flour (mg/100 g). Here are the data.
The loss of Vitamin C over time is clear, but with only 2 loaves of bread for each storage time we wonder if the differences among the groups are significant.
(a) 1. Use the Kruskal-Wallis test to assess significance, then write a brief summary of what the data show.
2. What is the p-value?
(a). 05 < p-value < .10
(b). 01 < p-value < .025
(c).025 < p-value < .05
(d). p-value < .005
(e). p-value > .10
(f).005 < p-value < .01
3.Summary of experiment: (check all that apply)
(a)The p-value does not indicate that there is strong evidence that vitamin C is systematically higher for some conditions after baking the bread than for other conditions
(b) p-value indicates that there is strong evidence that vitamin C is systematically higher for some conditions after baking the bread than for other conditions
(c) data show a pronounced decrease in vitamin C as the number of days after baking increases
(d) data show a pronounced increase in vitamin C as the number of days after baking increases.
4.Because there are only 2 observations per group, we suspect that the common chi-square approximation to the distribution of the Kruskal-Wallis statistic may not be accurate. The exact p-value (from the SAS software) is p = 0.0011. Compare this with your p-value from (a). Is the difference large enough to affect your conclusion? (check all that apply)
(a) p-value in part (a) is larger than the exact p-value of 0.0011
(b) difference between the approximate and exact p-values is not large enough to affect our conclusions
(c) difference between the approximate and exact p-values is large enough to affect our conclusions
(d) p-value in part (a) is smaller than the exact p-value of 0.0011.
Condition Vitamin C (mg/100g) Immediately after baking 47.62 49.79 One day after baking 40.45 43.46 Three days after baking 21.25 22.34 Five days after baking 13.18 11.65 Seven days after baking 8.51 8.13Explanation / Answer
Assume that there is no Vitamin C lost.
Then the null hypothesis is
H0: mimmediate = m3-day
Ha: mimmediate > m3-day
Summary statistics:
Column
n
Mean
Variance
Std. Dev.
Std. Err.
Immediate
2
48.705
2.35445
1.5344217
1.085
3-days
2
21.795
0.59405
0.7707464
0.545
Test Statistic: t = = 22.17. P(xbarimmediate – xbar3day > 26.91) = P(t > 22.16)
= 0.0039.
p-value is 0.0039.
Hypothesis test results:
?1 : mean of Immediate
?2 : mean of 3-days
?1 - ?2 : mean difference
H0 : ?1 - ?2 = 0
HA : ?1 - ?2 > 0
(without pooled variances)
Difference
Sample Mean
Std. Err.
DF
T-Stat
P-value
?1 - ?2
26.91
1.214187
1.4744174
22.16298
0.0039
t = 22.163; P = .0039; Conclusion: We have very strong evidence (P = .0039) that bread tends to lose vitamin C when stored after baking.
let t* = 6.192
The mean vitamin C level for the freshly-baked bread in the study was 26.91 mg/100 g higher than that of the 3-day-old bread. We are 90% confident that 3-day-old bread loses between 22.333 and 31.487 mg/100 g of vitamin C, on average, when compared to freshly baked bread.
Column
n
Mean
Variance
Std. Dev.
Std. Err.
Immediate
2
48.705
2.35445
1.5344217
1.085
3-days
2
21.795
0.59405
0.7707464
0.545
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