Download Does bread lose its vitamins when stored? Small loaves of bread

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 three days and then the vitamin C content was measured. The units are milligrams per
hundred grams of flour (mg/100g). Here are the data:
Immediately after baking:
Three days after baking:
47.62
21.25
49.79
22.34
a). When bread is stored, does it lose vitamin C? To answer this question, perform a two-sample t test for these data. Be
sure to state your hypotheses, the test statistic with degrees of freedom, and the P-value.
b). Give a 90% confidence interval for the amount of vitamin C lost.
(a) n1 = n2 = 2, x1-bar = 48.705, s1 = 1.5344,
x2-bar = 21.795, s2 = 0.7707
H0: Bread does not lose its vitamins when stored,
that is, x1-bar – x2-bar = 0
Ha: Bread loses its vitamins when stored, that is
x1-bar > x2-bar or x1-bar – x2-bar > 0
Right-tailed t- test with 1 degree of freedom,
 = 0.10; Critical t- value = 1.8856
Decision Rule: Reject H0 if the t- value for the
sample > 1.8856
SE = [s1^2 /n1 + s2^2 /n2]
= [1.5344^2 /2 + 0.7707^2 /2] = 1.2142
t = D/SE = (x1-bar – x2-bar)/SE
= (48.705 – 21.795)/1.2142 = 22.1635
Since 22.1635 > 1.8856, we reject H0 and
accept Ha
Conclusion: Bread loses its vitamins when stored.
[p- value corresponding to  = 0.10 and 1 degree
of freedom = 0.0010148]
(b) The 90% CI for the difference in the vitamin
content = D  1.645 * SE
The CI is 26.91  1.645(1.2142) = [24.9126 mg,
28.9074 mg].
t Test for Differences in Two Means
Data
Hypothesized Difference
Level of Significance
Population 1 Sample
Sample Size
Sample Mean
Sample Standard Deviation
Population 2 Sample
Sample Size
Sample Mean
Sample Standard Deviation
Intermediate Calculations
Population 1 Sample Degrees of
Freedom
Population 2 Sample Degrees of
Freedom
Total Degrees of Freedom
Pooled Variance
Difference in Sample Means
t Test Statistic
Upper-Tail Test
Upper Critical Value
p-Value
Reject the null hypothesis
0
0.1
2
48.705
1.5344
2
21.795
0.7707
1
1
2
1.4741809
26.91
22.163498
1.8856181
0.0010148