Question

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

2424

miles per gallon. To see if the goal is being​ met, they check the gasoline usage for

5050

company trips chosen at​ random, finding a mean of

22.0522.05

mpg and a standard deviation of

5.555.55

mpg. Is this strong evidence they have failed to attain their fuel economy​ goal? Complete parts a through e below.

​a) Write appropriate hypotheses.

Which hypotheses below will test if the company failed to attain their​ goal?

A.

Upper H 0H0​:

muμequals=2424

Upper H Subscript Upper AHA​:

muμnot equals≠2424

B.

Upper H 0H0​:

muμless than<2424

Upper H Subscript Upper AHA​:

muμequals=2424

C.

Upper H 0H0​:

muμgreater than>2424

Upper H Subscript Upper AHA​:

muμequals=2424

D.

Upper H 0H0​:

muμnot equals≠2424

Upper H Subscript Upper AHA​:

muμequals=2424

E.

Upper H 0H0​:

muμequals=2424

Upper H Subscript Upper AHA​:

muμgreater than>2424

F.

Upper H 0H0​:

muμequals=2424

Upper H Subscript Upper AHA​:

muμless than<2424

​b) Are the necessary assumptions to perform inference​ satisfied?

A.

​No, the nearly normal condition is not satisfied.

B.

​No, the randomization condition is not satisfied.

C.

​No, the​ 10% condition is not satisfied.

D.

​Yes, all the necessary assumptions are satisfied or can be assumed to be satisfied.

​c) Test the hypothesis and find the​ P-value.

The​ P-value is

nothing.

​(Round to three decimal places as​ needed.)

​d) Explain what the​ P-value means in this context.

Choose the correct answer below.

A.The​ P-value is the probability of obtaining a sample mean of

22.0522.05

mpg or more if the mean mileage of the fleet is

2424

mpg.

B.The​ P-value is the probability that the mean mileage of the fleet is greater than or equal to the proposed mean of

2424

mpg.

C.The​ P-value is the probability that the mean mileage of the fleet is

22.0522.05

mpg rather than the proposed mean of

2424

mpg.

D.The​ P-value is the probability of obtaining a sample mean of

22.0522.05

mpg or less if the mean mileage of the fleet is

2424

mpg.

​e) State an appropriate conclusion.

Since the​ P-value is

▼

less

greater

than any reasonable level of​ significance, the data

▼

provide

fail to provide

sufficient evidence to reject the null hypothesis.

Answer 1