Question

(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 the source data cannot be verified, the accuracy of these estimates are not guaranteed. Report all answers to 4 decimal places.

1. We would like to use these data to evaluate the average gas mileage of all 2012 Prius drivers. Do you think this is reasonable? Why or why not?

? Yes No , because  ? the data distribution seems approximately normal there are 14 data points in the sample user estimates are reliable user estimates are not reliable .

The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? Conduct a hypothesis test. Round numeric answers to 3 decimal places where necessary.

2. What are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? (Reminder: check conditions)

A. ?0:?=50H0:μ=50 vs. ??:?≠50HA:μ≠50
B. ?0:?=50H0:μ=50 vs. ??:?>50.3HA:μ>50.3
C. ?0:?=53.3H0:μ=53.3 vs. ??:?≠53.3HA:μ≠53.3
D. ?0:?=50.3H0:μ=50.3 vs. ??:?<50HA:μ<50

3. Calculate the test statistic.

4. Calculate the p-value.

5. How much evidence do we have that the null model is not compatible with our observed results?

A. some evidence
B. little evidence
C. extremely strong evidence
D. strong evidence
E. very strong evidence

6. Calculate a 95% confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov.

( ,  )

Answer 1

using excel>addin>phstat>onesample t

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	50
Level of Significance	0.05
Sample Size	14
Sample Mean	53.3
Sample Standard Deviation	5.2
Intermediate Calculations
Standard Error of the Mean	1.389758458
Degrees of Freedom	13
t Test Statistic	2.374513342
Two-Tail Test
Lower Critical Value	-2.160368656
Upper Critical Value	2.160368656
p-Value	0.033651112
Reject the null hypothesis

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	5.2
Sample Mean	53.3
Sample Size	14
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	1.389758458
Degrees of Freedom	13
t Value	2.160368656
Interval Half Width	3.002390613
Confidence Interval
Interval Lower Limit	50.30
Interval Upper Limit	56.30

Ans 1 ) yes because   the data distribution seems approximately normal there are 14 data points in the sample user estimates are reliable .

Ans2 ) A. ?0:?=50vs. HA:μ≠50

3. the test statistic. t=2.3745

4. the p-value. =0.0337

5
D. strong evidence

6. a 95% confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov. is (50.30,56.30)