15.28 Vitamins in bread. Does bread lose its vitamins when stored? Here are data on the vitamin C content (milligrams per 100 grams of flour) in bread baked from the same recipe and stored for one, three, five, or seven days. The 10 observations are from 10 different loaves of bread.

Condition Vitamin C (mg/100 g)

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 The loss of vitamin C over time is clear, but with only two loaves of bread for each storage time, we wonder if the differences among the groups are significant.

a. Use the Kruskal-Wallis test to assess significance and then write a brief summary of what the data show.

b. Because there are only two 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-

15 16 value (from SAS software) is P=0.0011 . Compare this with your P-value from part (a). Is the difference large enough to affect your conclusion?