Read the following scenario
and complete each of the seven problems below:
A new car manufacturing company has emerged
and has claimed that its new hybrid car, the Pusho, gets a better gas mileage
than the highest ranked Toyota Prius. Consumer Reports Magazine decides to test
this claim at a 5% level of significance. Consumer Reports randomly selects 10
of each type of car, calculates the miles per gallon for each car in the study,
and records the data in the table below. Assume miles per gallon of the cars is
normally distributed.
|
Pusho |
54.1 |
52.4 |
55.7 |
49.7 |
50.6 |
48.9 |
51.8 |
54.5 |
56.9 |
49.8 |
|
Prius |
53.2 |
54.3 |
49.8 |
50.1 |
50.5 |
56.1 |
47.8 |
53.4 |
56.8 |
48.7 |
A. Evaluate the claim that the Pusho gets a better gas mileage than
the highest ranked Prius using the data from the Consumer Reports study.
1. Identify the type of test you will use to test this claim. Explain
your reasoning.
2. State the null and alternate hypotheses.
3. Conduct the hypothesis test and determine the p-value.
4. State your conclusion about the claim.
5. Construct a 90% confidence interval for this study.
1.
2.
3.
4.
5.
Suppose that Toyota makes a counter-claim
that their Prius has a higher gas mileage than Pusho.
How could the alternative hypotheses from
Part A be changed to test Toyota’s claim?
Conduct the hypothesis test at the 5% level
of significance for Toyota’s claim using the data above and determine the
p-value.
State your conclusion about the claim.
Construct a 98% confidence interval for
this study.
1.
2.
3.
4.
C.
Based on your analysis of both claims from the makers of Pusho and
Prius, what statement can be made about the miles per gallon of the two cars?
Explain your reasoning.
<Compose
response here>
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