A recent study of peanut allergies—the LEAP trial—explored the relationship between early exposure to peanuts and the subsequent development of an allergy to peanuts. Infants (4 to 11 months old) who had shown evidence of other kinds of allergies were randomly assigned to one of two groups. Group 1 consumed a baby-food form of peanut butter. Group 2 avoided peanut butter. At 5 years old, 10 of 307 children in the peanut-consumption group were allergic to peanuts, and 55 of 321 children in the peanut-avoidance group were allergic to peanuts.

a. Does this study provide convincing evidence of a difference at the α =  0.05 significance level in the development of peanut allergies in infants like the ones in this study who consume or avoid peanut butter?

b. Based on your conclusion in part (a), which mistake— a Type I error or a Type II error—could you have made? Explain your answer.

c. Should you generalize the result in part (a) to all infants? Why or why not?