Question: Suppose I independently choose 100 forwards and 400 guards of NBA players, obtaining an average weight for the 100 forwards of 220 pounds, with a standard deviation (for those 100) of 30 pounds, an average weight for the 400 guards of 170 pounds, with a standard deviation (for those 400) of 25 pounds.

Test, at significance level 0.01, using a P-value, a basketball fan's assertion that forwards, on the average, are more than 40 pounds heavier than guards. Make no assumptions about population standard deviations. Conclude with a statement about whether or not the assertion is true.