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.

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

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.

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step-by-step explanation:

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