Question

In recent years major league baseball games have averaged three hours in duration. However, because games in Denver tend to be high-scoring, it might be expected that the games would be longer there. In 2018, the 81 games in Denver averaged 185.54 minutes with standard deviation 24.6 minutes. What would you conclude?

Answer 1

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, $\bar{x}$ = 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

$H_{0}: \mu = 180\text{ minutes}\\H_A: \mu > 18\text{ minutes}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{185.54 - 180}{\frac{24.6}{\sqrt{81}} } = 2.026$

Now,

$t_{critical} \text{ at 0.05 level of significance, 80 degree of freedom } = 1.664$

Since,                      

$t_{stat} > t_{critical}$

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.