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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 8.13

Explanation / 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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