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 41.4 mpg or better for their fleet of cars. To see if the goal is being​ met, they check the gasoline usage for 40 company trips chosen at​ random, finding a mean of 42.40 mpg and a standard deviation of 2.46 mpg. Is this strong evidence that they have attained their fuel economy​ goal? Complete parts​ (a) through​ (f) below. Use 0.05 as the​ P-value cutoff level.

Find the​ P-value.

Explain what the​ P-value means in this context. Choose the correct answer below.

The probability of observing a sample mean lower than 41.40 is 0.1%, assuming the data come from a population that follows a Normal model.

b. The probability of observing a sample mean higher than 38.4is 0.1%, assuming the data come from a population that follows a Normal model.

c. If the average fuel economy is 38.4mpg, the chance of obtaining a sample mean of 41.40 or more by natural sampling variation is 0.1%.

d. If the average fuel economy is 41.40 mpg, the chance of obtaining a population mean of 38.4 or more by natural sampling variation is 0.1​%.

​State an appropriate conclusion. Choose the correct answer below.

a. Reject the null hypothesis. There is not strong evidence that the company is meeting their goal.

b.Reject the null hypothesis. There is strong evidence that the company is meeting their goal.

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

d. Fail to reject the null hypothesis. There is strong evidence that the company is meeting their goal.

Answer 1

The p-value is we have Till t= 5TSh given significance level solution from the given information, we M= 41.4 mpg, 7=42.40 mpg, s=2.46 and nauo Null hypothests, Ho: 42 U14 Alternative hypothes pc. He'MC3317 level of signiffcause d20.05 The Test statisticas 42.40-uly to 2.46 l suo dfanat =40-1 [df =39 P-value=0.0049 It as observet that, the p-value is less than the * ophon @ es correct? fuel ecooomy goal is less than 4.40 mp 27 option bes correet: we refect the null hypotheses, *please rate It = 2-58 The degrees of freedomis