Fumonisins are environmental toxins produced by a type of mold and have been found in corn and in products made from raw corn. The Center for Food Safety and Applied Nutrition provided recommendations on allowable fumonisin levels in human food and in animal feed based on a study of corn meal. The study compared corn meal made from partially degermed corn (corn that has had the germ, the part of the kernel located at the bottom center of the kernel that is used to produce corn oil, partially removed) and corn meal made from corn that has not been degermed. Specimens of corn meal were analyzed and the total fumonisin level (ppm) was determined for each specimen. Summary statistics for total fumonisin level from the U.S. Food and Drug Administration's web site are given here.

a. If the given means and standard deviations had been based on a random sample of 10 partially degermed specimens and a random sample of 10 specimens made from corn that was not degermed, explain why it would not be appropriate to carry out a two-sample t test to determine if there is a significant difference in the mean fumonisin level for the two types of corn meal.

b. Suppose instead that each of the random samples had included 50 corn meal specimens. Explain why it would now be reasonable to carry out a two-sample t test.

c. Assuming that each random sample size was 50, carry out a test to determine if there is a significant difference in mean fumonisin level for the two types of corn meal. Use a significance level of .01.