Question

An automobile manufacturer has given its van a 54.5 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 220 vans, they found a mean MPG of 54.2. Assume the population variance is known to be 4.84. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

The test statistic value is -0.92.

Explanation:

In this case we need to test whether the van has an incorrect manufacturer's MPG rating.

The hypothesis can be defined as follows:

H₀: The manufacturer's MPG rating for the van is 54.5, i.e. μ = 54.5.

Hₐ: The manufacturer's MPG rating for the van is 54.5, i.e. μ ≠ 54.5.

The information provided is:

`n=220\\\bar x=54.2\\\sigma=4.84\\\alpha =0.01`

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

`z=(\bar x-\mu)/(\sigma/√(n))=(54.2-54.5)/(4.84/√(220))=-0.92`

The test statistic value is -0.92.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

`p-value=2\ P(Z<-0.92)\\=2* 0.17879\\=0.35758\\\approx 0.36`

*Use a z-table for the probability.

The p-value of the test is 0.36.

The p-value of the test is very large.

p-value = 0.36 > α = 0.01

The null hypothesis will not be rejected.

Thus, it can be concluded that the manufacturer's MPG rating for the van is 54.5 miles/gallon.