Question

Football Air Pressure During the National Football League’s 2014 AFC championship 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. Assuming this is a representative sample of all footballs used by the Patriots in the 2014 season, perform the appropriate test to determine if the average air pressure in footballs used by the Patriots was significantly less than the allowable limit of 12.5 psi. There is no extreme skewness or outliers in the data, so it is appropriate to use the t-distribution.(a) Clearly state the null and alternative hypotheses.

Answer 1

The null hypothesis is:
`H_0 :\mu = 12.5`

The alternative hypothesis is:
`H_a :\mu <12.5`

Explanation:

Consider the provided information.

It is given that the average air pressure in footballs used by the Patriots was significantly less than the allowable limit of 12.5 psi.

The null hypothesis indicates that there is no substantial difference between given populations, due to sampling or experimental error, any observed difference.

Therefore, the null hypothesis is:
`H_0 :\mu = 12.5`

The required alternative hypothesis is:
`H_a :\mu <12.5`