The owner of a service station wants to determine if owners of new cars (two years old or less) change their car’s oil more frequently than owners of older cars (more than two years old). From his records he takes a sample of new cars and a sample of older cars and determines the number of times the oil was changed in the last 12 months. The data is as follows and the attached printout is provided for your use. New : 4, 3, 3, 2, 4, 3, 2 Old : 4, 2, 1, 2, 3, 2, 1 At 5% level of significance, Do these data allow the service manager to conclude that new car owners change their car’s oil, on the average, more frequently than older car owners? a. There is not sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners. b. There is not sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners when in fact such evidence may exist. c. There is sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners when in fact such evidence may not exist. d. There is sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners. e. The significance level here does not provide enough information to make a conclusion. What type of error is possible? a. Type I. b. Type II. c. Rejection region. d. P-value. e. No error has been committed. The 95% confidence interval for estimating the difference in the actual average number of oil changes by the owners of new cars and owners of older cars is: a. (-0.049,1.763). b. (-0.251,1.965). c. (-0.506,2.220). d. (-0.696,2.410). e. cannot be determined by the information provided. Which of the following is the correct interpretation of the 95% confidence interval estimation? a. Through random sampling of the same size, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain Mu1 - Mu2. b. Through random sampling, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain Mu1 - Mu2. c. Through sampling of the same size, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain Mu1 - Mu2. d. Through random sampling of the same size, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain (-0.251,1.965). e. none of the above is a correct interval estimation interpretation.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The owner of a service station wants to determine if owners of new cars (two years old or less) change their car’s oil more frequently than owners of older cars (more than two years old). From his records he takes a sample of new cars and a sample of older cars and determines the number of times the oil was changed in the last 12 months. The data is as follows and the attached printout is provided for your use.
New : 4, 3, 3, 2, 4, 3, 2
Old : 4, 2, 1, 2, 3, 2, 1
At 5% level of significance, Do these data allow the service manager to conclude that new car owners change their car’s oil, on the average, more frequently than older car owners?
| a. |
There is not sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners. |
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| b. |
There is not sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners when in fact such evidence may exist. |
|
| c. |
There is sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners when in fact such evidence may not exist. |
|
| d. |
There is sufficient evidence to conclude that new car owners change their car's oil, on the average, more frequently than older car owners. |
|
| e. |
The significance level here does not provide enough information to make a conclusion. |
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What type of error is possible?
a. Type I.
b. Type II.
c. Rejection region.
d. P-value.
e. No error has been committed.
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The 95% confidence interval for estimating the difference in the actual average number of oil changes by the owners of new cars and owners of older cars is:
a. (-0.049,1.763).
b. (-0.251,1.965).
c. (-0.506,2.220).
d. (-0.696,2.410).
e. cannot be determined by the information provided.
Which of the following is the correct interpretation of the 95% confidence
interval estimation ?a. Through random sampling of the same size, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain Mu1 - Mu2.
b. Through random sampling, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain Mu1 - Mu2.
c. Through sampling of the same size, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain Mu1 - Mu2.
d. Through random sampling of the same size, multiple confidence intervals may be constructed. We expect 95% of the confidence intervals to contain (-0.251,1.965).
e. none of the above is a correct interval estimation interpretation.
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