Question

Some people believe that higher-octane fuels result in better gas mileage for their car. To test this claim, a researcher randomly selected 11 individuals to participate in the study. Each participant received 10 gallons of gas and drove his car on a closed course. The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine whether the car was filled up with 87-octane or 92-octane first, and the driver did not know which fuel was in the tank. Complete parts (a) through (e). Click here to view the data, probability plots, and technology output. LOADING... Click here to view the table of critical values for the correlation coefficient. LOADING... (a) Why is it important that the matching be done by driver and car? A. How someone drives and the car they drive result in different fuel consumption. B. It allows each driver to determine which fuel is best for their car. C. It allows all of the trials to be done at the same time. D. It cuts the cost of doing the research. (b) Why is it important to conduct the study on a closed track? A. So that the researcher can watch the drivers B. So that each car travels the same distance C. So that all drivers and cars have similar driving conditions D. So that each car uses the same amount of gas (c) The normal probability plots and linear correlation coefficients for miles on 87-octane and miles on 92-octane are given. The correlation between 87 octane and the expected z-scores is 0.876. The correlation between 92 octane and the expected z-scores is 0.878. Are either of these variables normally distributed? A. No, neither variable is normally distributed. B. Yes, 92-octane is normally distributed. C. Yes, both variables are normally distributed. D. Yes, 87-octane is normally distributed. (d) The differences are computed as 92-octane minus 87-octane. The normal probability plot of the differences is shown. The correlation between the differenced data and the expected z-scores is 0.951. Is there reason to believe that the differences are normally distributed? ▼ No, Yes, since the ▼ correlation coefficient slope of the line is ▼ greater than less than equal to ▼ 0. the critical value. 0.5. 1. (e) The researchers used a statistical software package to determine whether the mileage from 92-octane is greater than the mileage from 87-octane. What do you conclude at alphaequals0.05? Why? Begin by writing the hypotheses. Upper H 0: The difference in mileage for 92-octane and 87-octane ▼ is greater than is different from equals is less than zero. Upper H 1: The difference in mileage for 92-octane and 87-octane ▼ is less than equals is different from is greater than zero. The test statistic is nothing. (Do not round.) The P-value is nothing. (Do not round.) Therefore, there ▼ is is not sufficient evidence that the mileage from 92-octane ▼ is the same as is different from is greater than is less than the mileage from 87-octane. Click to select your answer(s).

Answer #1

**a)**

How someone drives and the car they drive result in different fuel consumption

**b)**

So that all drivers and cars have similar driving conditions

**c)**

Histogram for 87 octance

Histogram for 92 octance

No, neither variable is normally distributed.

**d)** Yes, since the slope of the line correlation
coefficient is less than the critical value of 0.05.

**e)**

H0: The difference in mileage for 92-octane and 87-octane
**equals** zero. Upper

H1: The difference in mileage for 92-octane and 87-octane
**is greater** than zero.

The test statistic is **1.02228801640586** (Do
not round.) The P-value is **.165389** (Do not
round.) Therefore, there **is not** sufficient
evidence that the mileage from 92-octane **is
greater** than from the mileage from 87-octane.

The mean gas mileage for a hybrid car is 56 miles per gallon.
Suppose that the gasoline mileage is approximately normally
distributed with a standard deviation of
3.3 miles per gallon.
(a) What proportion of hybrids gets over 61 miles per
gallon?
(b) What proportion of hybrids gets 52 miles per gallon or
less?
(c) What proportion of hybrids gets between 59 and 62 miles per
gallon?
(d) What is the probability that a randomly selected hybrid gets
less than...

A car company claims that the mean gas mileage for its luxury
sedan is at least 24 miles per gallon. A random sample of 7 cars
has a mean gas mileage of 23 miles per gallon and a standard
deviation of 2.4 miles per gallon. At α=0.05, can you support the
company’s claim assuming the population is normally distributed?
Yes, since the test statistic is not in the rejection region
defined by the critical value, the null is not rejected....

A certain model of automobile has its gas mileage (in miles per
gallon, or mpg) normally distributed, with a mean of 32 mpg and a
standard deviation of 4 mpg. Find the probability that a car
selected at random has the following gas mileages. (Round your
answers to four decimal places.) (a) less than 26 mpg (b) greater
than 34 mpg (c) between 30 and 34 mpg

A car company claims that its cars achieve an average gas
mileage of at least 26 miles per gallon. A random sample of eight
cars form this company have an average gas mileage of 25.2 miles
per gallon and a standard deviation of 1 mile per gallon. At
α=0.06, can the company’s claim be supported, assuming this is a
normally distributed data set?
a) No, since the test statistic of -2.26 is in the rejection
region defined by the critical...

The gas mileage for a particular type of car is known to have a
standard deviation σ = 1 mile. For a fixed speed (65 miles/hour)
sixteen cars were tested and found to get an average of 24.3 miles
per gallon. What is the z-test statistic for the null hypothesis
H0: μ = 25 miles per gallon?
a.
-.7 b.
-1.4
c.
-2.8 d. 1.4
If the z-test statistic for H0: μ = 10 yields a
p-value of .03. Should...

Gas Mileage
The cost of fuel is largest component of cost of ownership for
most vehicles. Fuel cost is (almost) inversely proportional to gas
mileage; higher gas mileage means lower fuel cost and vice-versa.
If you keep track of the number of miles driven on each tank of gas
as well as how much gas is purchased, it is easy to calculate gas
mileage; many cell phone apps exist to track this. The data on the
second page is the...

In a recent publication, it was reported that the average
highway gas mileage of tested models of a new car was 33.2 mpg and
approximately normally distributed. A consumer group conducts its
own tests on a simple random sample of 17 cars of this model and
finds that the mean gas mileage for their vehicles is 31.5 mpg with
a standard deviation of 3.5 mpg. Perform a test at the level to
determine if these data support the contention that...

A new car that is a gas- and electric-powered hybrid has
recently hit the market. The distance travelled on 1 gallon of fuel
is normally distributed with a mean of 65 miles and a standard
deviation of 7 miles. Find the probability of the following
events:
A. The car travels more than 69 miles per gallon.
Probability =
B. The car travels less than 57 miles per gallon.
Probability =
C. The car travels between 60 and 69 miles per...

A statistics instructor wonders whether significant differences
exist in her students’ test scores in her three different sections.
She randomly selects the scores from 10 students in each section. A
portion of the data is shown in the accompanying table. Assume test
scores are normally distributed.
Click here for the Excel Data File
Click here for the CSV Data File
Section 1
Section 2
Section 3
93
84
56
54
71
93
⋮
⋮
⋮
93
50
96
a. Construct...

16. In a hypothesis test, the claim is μ≤28 while the sample of
29 has a mean of 41 and a standard deviation of 5.9. In this
hypothesis test, would a z test statistic be used or a t test
statistic and why?
z test statistic would be used as the mean is less than than
30
t test statistic would be used as the sample size is less than
30
t test statistic would be used as the standard...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 2 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 24 minutes ago

asked 26 minutes ago

asked 39 minutes ago

asked 47 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago