Answer:
We conclude that there is enough evidence to claim that the van has a 31.3 miles/gallon (MPG) rating.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 31.3 miles/gallon
Sample mean, [tex]\bar{x}[/tex] = 31.1
Sample size, n = 140
Alpha, α = 0.02
Population standard deviation, σ = 1.3
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 31.3\text{ miles/gallon}\\H_A: \mu \neq 31.3\text{ miles/gallon}[/tex]
We use Two-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{31.1 - 31.3}{\frac{1.3}{\sqrt{140}} } = -1.82[/tex]
Now, [tex]z_{critical} \text{ at 0.02 level of significance } = \pm 2.33[/tex]
Since,
The calculated z-statistic lies in the acceptance region, we fail to reject the null hypothesis and accept it.
We conclude that there is enough evidence to claim that the van has a 31.3 miles/gallon (MPG) rating.
