A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have failed to attain their fuel economy goal?

Question

A.) Write appropriate hypothesis

B.) Are there necessary assumptions to make inferences satisfied?

C.) Describe the sampling distribution models of mean fuel economy for samples like this.

D.) Find the P- Value

E.) Explain what the p-vale means in this context?

F.) State an appropriate conclusion.

Answer 1

I'll give a few hints and let you take it from there.

Hypotheses:
Ho: µ ≥ 26
Ha: µ < 26

Try a z-test to determine the test statistic.

Formula:
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

With your data:
z = (25.02 - 26)/(4.83/√50)

Finish the calculation.

Once you have the z-test statistic, check a z-table for the p-value. The p-value is the actual level of the test statistic.

Determine your conclusion. If the null (Ho) is not rejected, there is no difference. If the null is rejected, accept Ha and conclude a difference.

I hope this will help.

Answer 2

t-test is used because it is quantitative, z-test is used for categorical for these type of stats.

Answer 3

Step 1: Hypotheses:
Ho: µ ≥ 26
Ha: µ < 26

Step 2: One sample T- test
t = (ȳ - µ) / (s/√ n)

Step 3: P- Value method
tcdf(p-value, 99,df)

Step 4: reject or not reject null hypothesis