Newscientist.com ran the headline ‘‘Breakfast Cereals Boost Chances of Conceiving Boys,” based on an article which found that women who eat breakfast cereal before becoming pregnant are significantly more likely to conceive boys. The study used a significance level of α = 0.01. The researchers kept track of 133 foods and, for each food, tested whether there was a difference in the proportion conceiving boys between women who ate the food and women who didn’t. Of all the foods, only breakfast cereal showed a significant difference.

(a) If none of the 133 foods actually have an effect on the gender of a conceived child, how many (if any) of the individual tests would you expect to show a significant result just by random chance? Explain.

(b) Do you think the researchers made a Type I error? Why or why not?

(c) Even if you could somehow ascertain that the researchers did not make a Type I error, that is, women who eat breakfast cereals are actually more likely to give birth to boys, should you believe the headline ‘‘Breakfast Cereals Boost Chances of Conceiving Boys”? Why or why not?