Xr13-152 In 2005 Larry Summers, then president of Harvard University, received an avalanche of criticism for his attempt to explain why there are more male professors than female professors in mathematics.

He suggested that there were innate differences that might permanently thwart the search for a more perfect gender balance. In an attempt to refute Dr. Summers’s hypothesis, several researchers conducted large-scale mathematics tests of male and female students. Suppose the results were recorded.

Conduct whatever tests you deem necessary to draw conclusions from these data. (Note: The data are simulated but represent actual results.)

Exercises 13.153 and 13.154 require access to the data files introduced in previous exercises.