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During the National Football League's 2014 AFC charhpionship game, officials measured the air pressure on 11 of the game footballs being used by the New England Patriots. They found that the balls had an average air pressure of 11.1 psi, with a standard deviation of 0.40 psi. Find the test statistic

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Answer:

The test statistic for this situation is calculated using the following formula:

t = (Mean - Hypothesized Mean) / (Standard Error)

In this case, the hypothesized mean is the standard air pressure for an NFL football, which is 12.5 psi. The standard error is calculated as follows:

Standard Error = Standard Deviation / √(Sample Size)

Plugging in the values:

Standard Error = 0.40 psi / √(11) = 0.1225 psi

Now we can calculate the test statistic:

t = (11.1 psi - 12.5 psi) / 0.1225 psi = -1.40

Since the calculated test statistic is -1.40, it indicates that there is not a significant difference between the average air pressure of the footballs used by the New England Patriots and the standard air pressure for an NFL football.

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