Mathematics: An automobile manufacturer claims that its van has a 31.3 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this van since it is believed that the van has an incorrect manufacturer s mpg rating. after testing 140 vans, they found a mean mpg of 31.1. assume the standard deviation is known to be 1.3. a level of significance of 0.02 will be used. make a decision to reject or fail to reject the null hypothesis.

Step-by-ste p explanation:i need points s...

An automobile manufacturer claims that its van has

evanwall91

15.01.2022

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, $\bar{x}$ = 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

$H_{0}: \mu = 31.3\text{ miles/gallon}\\H_A: \mu \neq 31.3\text{ miles/gallon}$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{31.1 - 31.3}{\frac{1.3}{\sqrt{140}} } = -1.82$

Now, $z_{critical} \text{ at 0.02 level of significance } = \pm 2.33$

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.

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