Question

An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 47.0. Assume the population standard deviation is known to be 1.9. A level of significance of 0.02 will be used.

A. Find the value of the test statistic.
B. State the null and alternative hypotheses.

Answer 1

A

The test statistics is
`t = -1.7`

B

The Null and Alternative hypothesis are

`H_o : \mu = 47.2` and
`H_a : \mu \\e 47.2`

Explanation:

From the question we are told that

The population mean is
`\mu = 47.2 miles/gallon(MPG)`

The sample size is
`n = 250 \ van`

The sample mean is
`\= x = 47.0`

The sample standard deviation is
`\sigma = 1.9`

The level of significance is
`\alpha = 0.02`

Given that the value which the manufacturer gave the automobile is 47.2 and it is believed that this is not correct, then

The Null Hypothesis is

`H_o : \mu = 47.2`

The alternative Hypothesis is

`H_a : \mu \\e 47.2`

The test statistics can be mathematically evaluated as

`t = (\= x- \mu)/((\sigma )/(√(n) ) )`

substituting values

`t = (\= 47- 47.2)/((1.9 )/(√(250) ) )`

`t = -1.7`