Answer:
We conclude that the games in Denver would be longer than major league baseball games.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 180 minutes
Sample mean, [tex]\bar{x}[/tex] = 185.54 minutes
Sample size, n = 81
Alpha, α = 0.05
Sample standard deviation, s = 24.6 minutes
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 180\text{ minutes}\\H_A: \mu > 18\text{ minutes}[/tex]
We use one-tailed t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{185.54 - 180}{\frac{24.6}{\sqrt{81}} } = 2.026[/tex]
Now,
[tex]t_{critical} \text{ at 0.05 level of significance, 80 degree of freedom } = 1.664[/tex]
Since,
[tex]t_{stat} > t_{critical}[/tex]
We fail to accept the null hypothesis and reject it.
We accept the alternate hypothesis.
We conclude that the games in Denver would be longer than major league baseball games.
