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In the MLS, teams furnish the soccer balls they use for games. The soccer balls are supposed to be inflated to about 13 psi (lb/in2). The distribution of air pressure measurements approximates a normal distribution, with mean 13 and standard deviation 0.25.
The DC United has been accused of over-inflating their soccer balls to make them easier to kick. To check this claim, the MLS gathers a random sample of 10 soccer balls approved pre-game by the LA Galaxy, and they measure the psi for each. The average air pressure of the 10 balls comes out to 11 psi.
Conduct a test of significance to determine whether the difference would be great enough to be considered "statistically significant" (not explained by chance variation). Use an alpha-level of 0.05. and submit the hypotheses, define variables, and state the test statistic, p-value and conclusion. Draw the bell curve, and indicate the location of the sample mean.
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