Question
In: Statistics and Probability
Two types of engines are tested for fuel efficiency based on miles per gallon. A sample...
Two types of engines are tested for fuel efficiency based on miles per gallon. A sample of 31 cars were tested with Brand X and the mean was 20.9 mpg with a standard deviation of 1.8 mpg. 31 cars tested with Brand Y had a mean of 17.6 mpg and a standard deviation of 1.2 mpg. Test the claim that Brand X is more efficient than Brand Y. Use a 0.05 significance level.
Using the data from Problem #1, calculate a 99% confidence interval of the difference between fuel efficiencies of Brand X and Brand Y.
Solutions
Expert Solution
We don't whether population variances are equal or not. Although the sample size proportion is one but sample size is large. So large sample theory leads to take z variate. Otherwise we could take pooled variance for t variate.
orchestra answered 2 years agoRelated Solutions
The fuel efficiency, measured in miles per gallon, was measured for each of 12 cars when...
The fuel efficiency, measured in miles per gallon, was measured
for each of 12 cars when the cars where brand new. After exactly 5
years of use, the fuel efficiency of the same 12 cars was measured
again. The data is in the following table. Mileage when New Mileage
after 5 years Difference 16 15 1 27 24 3 17 17 0 33 29 4 28 25 3 24
22 2 18 16 2 22 20 2 20 21 -1...
Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types...
Engineers are testing company fleet vehicle fuel economy (miles
per gallon) performance by using different types of fuel. One
vehicle of each size is tested. Does this sample provide sufficient
evidence to conclude that there is a significant difference in
treatment means?
87 Octane
89 Octane
91 Octane
Ethanol 5%
Ethanol 10%
Compact
27.2
30.0
30.3
26.8
25.8
Mid-Size
23.0
25.6
28.6
26.6
23.3
Full-Size
21.4
22.5
22.2 ...
Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types...
Engineers are testing company fleet vehicle fuel economy (miles
per gallon) performance by using different types of fuel. One
vehicle of each size is tested. Does this sample provide sufficient
evidence to conclude that there is a significant difference in
treatment means?
87 Octane
89 Octane
91 Octane
Ethanol 5%
Ethanol 10%
Compact
30.4
29.7
16.0
30.0
29.8
Mid-Size
17.0
17.2
20.8
19.1
30.7
Full-Size
28.0
28.3
19.7
29.8
27.1
SUV
18.6
22.2
15.0
23.9
31.6
Click here for the...
Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types...
Engineers are testing company fleet vehicle fuel economy (miles
per gallon) performance by using different types of fuel. One
vehicle of each size is tested. Does this sample provide sufficient
evidence to conclude that there is a significant difference in
treatment means?
87 Octane
89 Octane
91 Octane
Ethanol 5%
Ethanol 10%
Compact
31.2
31.6
22.0
29.7
30.6
Mid-Size
17.3
17.6
18.9
17.2
28.2
Full-Size
27.2
28.1
15.9
31.9
29.7
SUV
20.0
22.0
20.7
23.6
31.4
(a) Choose the correct...
Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types...
Engineers are testing company fleet vehicle fuel economy (miles
per gallon) performance by using different types of fuel. One
vehicle of each size is tested. Does this sample provide sufficient
evidence to conclude that there is a significant difference in
treatment means?
87 Octane
89 Octane
91 Octane
Ethanol 5%
Ethanol 10%
Compact
30.8
28.4
17.7
30.7
31.1
Mid-Size
17.0
19.9
20.1
17.1
31.4
Full-Size
28.9
29.0
20.4
27.0
31.3
SUV
21.9
22.8
19.5
18.7
29.6
(b) Fill in the...
Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types...
Engineers are testing company fleet vehicle fuel economy (miles
per gallon) performance by using different types of fuel. One
vehicle of each size is tested. Does this sample provide sufficient
evidence to conclude that there is a significant difference in
treatment means?
87 Octane
89 Octane
91 Octane
Ethanol 5%
Ethanol 10%
Compact
30.8
28.4
17.7
30.7
31.1
Mid-Size
17.0
19.9
20.1
17.1
31.4
Full-Size
28.9
29.0
20.4
27.0
31.3
SUV
21.9
22.8
19.5
18.7
29.6
Click here for the...
The fuel consumption, in miles per gallon, of all cars of a particular model has a...
The fuel consumption, in miles per gallon, of all cars of a
particular model has a mean of 25 and a standard deviation of 2.
The population distribution can be assumed as normal. A random
sample of these cars is taken.
a. Find the probability that the sample mean fuel consumption
will be fewer than 24 miles per gallon if (i) a sample of 1
observation is taken, (ii) a sample of 4 observations if taken and
(iii) a sample...
Fuel consumption is commonly measured in miles per gallon (mi/gal). An agency designed new fuel consumption...
Fuel consumption is commonly measured in miles per gallon
(mi/gal). An agency designed new fuel consumption tests to be used
starting with 2008 car models. Listed below are randomly selected
amounts by which the measured MPG ratings decreased because of the
new 2008 standards. Find the range, variance, and standard
deviation for the sample data. Is the decrease of 4 mi/gal
unusual? Why or why not?
22
11
33
22
44
11
33
22
22
22
22
22
11
22 ...
Based on annual driving of 15,000 miles and fuel efficiency of 20 mpg, a car in...
Based on annual driving of 15,000 miles and fuel efficiency of
20 mpg, a car in the United States uses, on average, 700 gallons of
gasoline per year. If annual automobile fuel usage is normally
distributed, and if 26.76% of cars in the United States use less
than 480 gallons of gasoline per year, what is the standard
deviation?
Round your answer to 2 decimal places, the tolerance is
+/-0.05.
Featured below are data on fuel economy (in miles/gallon) for a random sample of 12 mid-size...
Featured below are data on fuel economy (in miles/gallon) for a
random sample of 12 mid-size cars.
X: {25.8, 20.2, 28.7, 24.6, 19.5, 33.1, 30.5, 27.7, 28.4, 30.9,
22.3, 24.2}
Construct a 95% confidence interval for the true mean fuel
economy
Conduct a test to determine whether the true mean is
higher than 25.0 miles/ gallon.
The null and alternative hypothesis
The test statistic
The p-value of the test,
Your decision and the interpretation in the context of the
problem.
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