Question

An automobile manufacturer has given its car a 54.6 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 140 cars, they found a mean MPG of 54.1. Assume the population standard deviation is known to be 2.4. A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Answer 1

They want to test if that the claimed MPG is incorrect (different from 54.6 MPG) and this claim needs to be on the alternative hypothesis, so then the system of hypothesis for this case are:

Null hypothesis:
`\mu = 54.6`

Alternative hypothesis:
`\mu \\eq 54.6`

Explanation:

For this case we define the random variable of interest X as the miles per gallon rating. And from a random sample of n = 140 cars we have the following info given:

`\bar X = 54.1`

`\sigma = 2.4`

They want to test if that the claimed MPG is incorrect (different from 54.6 MPG) and this claim needs to be on the alternative hypothesis, so then the system of hypothesis for this case are:

Null hypothesis:
`\mu = 54.6`

Alternative hypothesis:
`\mu \\eq 54.6`

And the statistic to check the hypothesis is given by:

`z= (\bar X- \mu)/((s)/(√(n)))`

And replacing we got:

`z = (54.1-54.6)/((2.4)/(√(140)))= -2.465`