Question

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel...

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer's calculations of miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer's and the driver's calculations for that random sample of 20 records. The driver wants to determine if these calculations are different. Assume that the standard deviation of a difference is

σ = 3.0.

5.0

7.5

−0.6

1.6

3.7

4.5

7.0

2.2

4.8

3.0

4.4

0.2

3.0

1.4

1.4

5.0

2.1

3.5

−0.6

−4.2

(a) State the appropriate

H0

and

Ha

to test this suspicion.

H0: μ = 3 mpg;    Ha: μ ≠ 3 mpg

H0: μ = 0 mpg;    Ha: μ ≠ 0 mpg

    

H0: μ < 0 mpg;    Ha: μ > 0 mpg

H0: μ > 3 mpg;    Ha: μ < 3 mpg

H0: μ > 0 mpg;    Ha: μ < 0 mpg


(b) Carry out the test. Give the P-value. (Round your answer to four decimal places.)


Interpret the result in plain language.

We conclude that μ ≠ 3 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.We conclude that μ ≠ 0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency does not differ from the driver's computed values.    We conclude that μ = 0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.We conclude that μ ≠ 0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.We conclude that μ = 3 mpg; that is, we have strong evidence that the computer's reported fuel efficiency does not differ from the driver's computed values.

Homework Answers

Answer #1

The statistical software output for this problem is:

One sample Z hypothesis test:
μ : Mean of variable
H0 : μ = 0
HA : μ ≠ 0
Standard deviation = 3

Hypothesis test results:

Variable n Sample Mean Std. Err. Z-Stat P-value
Data 20 2.745 0.67082039 4.0920044 <0.0001

Hence,

a) H0: μ = 0 mpg;    Ha: μ ≠ 0 mpg

Option B is correct.

b) P - value = 0.0000

c) We conclude that μ ≠ 0 mpg; that is, we have strong evidence that the computer's reported fuel efficiency differs from the driver's computed values.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Computers in some vehicles calculate various quantities related to performance. One of these is the fuel...
Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer's calculations of miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of...
Computers in some vehicles calculate various quantities related to performance. One of these is the fuel...
Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). A particular vehicle equipped in this way is advertised as having a fuel efficiency of 41 mpg. A woman who owns one of these vehicles believes she is getting even higher fuel efficiency, so she recorded the mpg each time the gas tank was filled, and then reset the computer. For 18 recordings,...
. Computers in some vehicles calculate various quantities related to performance. One of these is fuel...
. Computers in some vehicles calculate various quantities related to performance. One of these is fuel efficiency, or gas mileage, usually expresses as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank filled, and the computer was then reset. Here are the mpg values for a random sample of 20 of these records: 41.5 50.7 36.6 37.3 34.2 45.0 48.0 43.2 47.7 42.2 43.2 44.6 48.4 46.4...
The highway miles per gallon rating of the 1999 Volkswagen Passat was 31 mpg (Consumer Reports,...
The highway miles per gallon rating of the 1999 Volkswagen Passat was 31 mpg (Consumer Reports, 1999). The fuel efficiency that a driver obtains on an individual tank of gasoline naturally varies from tankful to tankful. Suppose the mpg calculations per tank of gas vary normally with a mean μ = 31 mpg and standard deviation σ = 3 mpg. According to the Central Limit Theorem, what would be the value of the mean of the sampling distribution if we...
HW9-Practice: Problem 3 Problem Value: 1 point(s). Problem Score: 50%. Attempts Remaining: Unlimited. (1 point) Fueleconomy.gov,...
HW9-Practice: Problem 3 Problem Value: 1 point(s). Problem Score: 50%. Attempts Remaining: Unlimited. (1 point) Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is 53.3 MPG and the standard deviation is 5.2 MPG. Note that these data are user estimates and since...
A driver recorded the miles per gallon by dividing the miles driven by the number of...
A driver recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer’s and the driver’s calculations for that random sample of 20 records. For example, the third value is -0.6. That might be a trip where the computer said the gas mileage was 48.1 and the driver computed it as 48.7, giving a difference of -0.6. The driver wants to determine whether the...
To test whether acetone improves fuel efficiency in passenger cars, 10 people were randomly selected. Each...
To test whether acetone improves fuel efficiency in passenger cars, 10 people were randomly selected. Each person brings his/her car to a gas station and fills it with gas. The car’s mileage is recorded. When the car is nearly empty, the person takes the car back to the gas station and refills it. Mileage and miles per gallon are recorded. Acetone is added to the tank. When the tank is nearly empty, the person returns to the gas station and...
Question 1 (1 point) Suppose the national average dollar amount for an automobile insurance claim is...
Question 1 (1 point) Suppose the national average dollar amount for an automobile insurance claim is $746.9. You work for an agency in Michigan and you are interested in whether or not the state average is different from the national average. Treating the national mean as the historical value, What are the appropriate hypotheses for this test? Question 1 options: 1) HO: μ ≤ 746.9 HA: μ > 746.9 2) HO: μ > 746.9 HA: μ ≤ 746.9 3) HO:...
The Nielsen Company is a global information and media company and one of the leading suppliers...
The Nielsen Company is a global information and media company and one of the leading suppliers of media information. In their state-of-the-media report, they announced that U.S. cell phone subscribers average 5.4 hours per month watching videos on their phones. We decide to construct a 95% confidence interval for the average time (hours per month) spent watching videos on cell phones among U.S. college students. We draw the following SRS of size 8 from this population. 11.8    2.7    3.0    6.1    4.8    9.8    11.2    7.7 We want to...
Question 13 (1 point) A statistics professor wants to examine the number of hours that seniors...
Question 13 (1 point) A statistics professor wants to examine the number of hours that seniors and freshmen study for the final. Specifically, the professor wants to test if the average number of hours that seniors study is greater than the average number of hours that freshmen study. If the seniors are considered group 1 and the freshmen are considered group 2, what are the hypotheses for this scenario? Question 13 options: 1) HO: μ1 = μ2 HA: μ1 ≠...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT