According to a psychologist at the Medical College of Virginia, soccer players who "head" the ball 10 or more times a game are at risk for brain damage that could lower their intellectual abilities. In tests involving young male soccer players, those who typically headed the ball 10 or more times a game recorded a mean IQ score of 103, compared to a mean of 112 for those who usually headed the ball once or less a game.
Assuming 30 players in each sample, with sample standard deviations of 17.4 and 14.5 IQ points for the "headers" and "nonheaders," respectively, use an appropriate one-tail z-test and the 0.01 level of significance in reaching a conclusion as to whether frequent "heading" of the ball by soccer players might lower intellectual performance.
Determine and interpret the p-value for the test.