Fuel efficiency of Prius: 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.
(a) 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?
Test at the αα = 0.05 level of significance.
The hypotheses for the test are:
- Ho: μ = 50
Ha: μ < 50
- Ho: μ = 50
Ha: μ > 50
- Ho: μ = 50
Ha: μ ≠ 50
To execute this hypothesis test we should use a:
because:
- σ is known and the population is normal
- σ is unknown and the sample size is less than 30
- σ is known, but the sample size is less than 30
There are degrees of freedom for this test.
The test statistic is: (please round to two decimal places)
The p-value for this hypothesis test is: (please round to three decimal places)
The conclusion for the hypothesis test is:
- Since p ≥ α we do not have enough evidence to reject the null hypothesis
- Since p ≥ α we reject the null hypothesis and accept the alternative
- Since p<α we reject the null hypothesis and accept the alternative
- Since p<α we fail to reject the null hypothesis
- Since p ≥ α we accept the null hypothesis
(c) Calculate a 95% confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov.
We are % confident that the true population gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov is between mpg and mpg. (please round to one decimal place)