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 38.2 mpg or better for their fleet of cars. To see if the goal is being​ met, they check the gasoline usage for 36 company trips chosen at​ random, finding a mean of 40.20 mpg and a standard deviation of 3.04 mpg.
Is this strong evidence that they have attained their fuel economy​ goal? Use 0.05 as the​ P-value cutoff level.

Answer 1

Answer:

The calculated value t= 3,947 >  2.0301 at 0.05 level of significance ( two tailed test) with 35 degrees of freedom.

Null hypothesis is rejected

There is no strong evidence that they have attained their fuel economy​ goal.

Step-by-step explanation:

Step (i):-

A company with a large fleet of cars hopes to meet the goal of 38.2 mpg or better for their fleet of cars.

Population mean 'μ' = 38.2mpg

Given the gasoline usage for 36 company trips chosen at​ random, finding a mean of 40.20 mpg and a standard deviation of 3.04 mpg.

Sample size 'n' = 36

mean  of the Sample 'x⁻' = 40.20mpg

standard deviation of the Sample 'S' = 3.04 mpg.

Step(ii):-

Null hypothesis: H₀: 'μ' = 38.2mpg

Alternative hypothesis: H₁: 'μ' ≠ 38.2mpg

Level of significance ∝=0.05

The test of hypothesis

                             $t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n} } }$

                            $t = \frac{40.20- 38.20}{\frac{3.04}{\sqrt{36} } } = 3.947$

The degrees of freedom ν= n-1 = 36-1 =35

The tabulated value t₀.₀₅ =  2.0301 at 0.05 level of significance ( two tailed test) with 35 degrees of freedom.

The calculated value t= 3,947 >  2.0301 at 0.05 level of significance ( two tailed test) with 35 degrees of freedom.

Null hypothesis is rejected

Conclusion:-

There is no strong evidence that they have attained their fuel economy​ goal.