Some people believe that math ability and musical ability have a relationship — that is, people with musical ability also seem to do well in math. A group of

researchers decides to test this theory. The researchers randomly select 100

musically gifted individuals and also 150 individuals with no musical talent.

Each individual is given a test for math ability. The results are shown below

. Run an appropriate test to see if the mean math-ability score for those who

are musically gifted is significantly higher than that of those who are not

musically gifted. Use a 1% level of significance. (22 points)

Let

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µu = mean math-ability score for those who are musically gifted

Let

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µn = mean math-ability score for those who are not musically gifted