Question

Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to meet the goal of 30.4 mpg or better for their fleet of cars. To see if the goal is being​met, they check the gasoline usage for 46 company trips chosen at ​random, finding a mean of 31.4 mpg and a standard deviation of 2.57 mpg. Is this strong evidence that they have attained their fuel economy​ goal? Use 0.05 as the​ level of significance. p-Value = 0.006.

State an appropriate conclusion. Choose the correct answer below.

		Fail to reject the null hypothesis. There is not strong evidence that the company is meeting their goal.
		Reject the null hypothesis. There is not strong evidence that the company is meeting their goal.
		Reject Reject the null hypothesis. There is strong evidence that the company is meeting their goal.
		Fail to reject the null hypothesis. There is strong evidence that the company is meeting their goal

Answer 1

Solution:

Given: A company with a large fleet of cars hopes to meet the goal of 30.4 mpg or better for their fleet of cars.

That is : Mean = mpg.

Sample size = n = 46

Sample mean =

Sample standard deviation = s = 2.57 mpg

We have to test if there is strong evidence that they have attained their fuel economy​ goal.

level of significance = 0.05

Step 1) State H0 and H1:

Vs

Step 2) Find test statistic:

Since population standard deviation is unknown we use t test statistic.

Step 3) Find p-value.

Use excel command:

=T.DIST.RT(x , degrees of freedom)

x = t = 2.639

df = degrees of freedom = n - 1= 46 - 1 =45

Thus

=T.DIST.RT( 2.639 , 45)

=0.00569

=0.006

Thus p-value = 0.006

Step 4) Decision Rule:

Reject H0, if p-value < 0.05 level of significance , otherwise we fail to reject H0.

Since p-value = 0.006 < 0.05 level of significance, we reject H0.

Step 5) Conclusion:

Since we have rejected null hypothesis H0, there is strong evidence that they have attained their fuel economy​ goal.