I am shopping for a new sedan and would like to get one with excellent miles per gallon (MPG). I heard that German cars tend to be more fuel efficient than American cars, so I collected MPG data on a random sample of 10 German 4-cylinder sedan models (listed in the table below) to be compared to the American car statistics. I would like to see if there is a significant difference, in either direction, between German sedans and American sedans. The US Environmental Protection Agency reported that the average MPG for American sedans in 2017 is ?? = 30.6. I set the significance level at α = .10 for a two-tailed hypothesis test. Hint: Because we know the population mean for the American cars but not the standard deviation, we cannot conduct a Z test but should perform a one-sample t-test instead.
Q1) One-Sample t-Test
I am shopping for a new sedan and would like to get one with excellent miles per gallon (MPG). I heard that German cars tend to be more fuel efficient than American cars, so I collected MPG data on a random sample of 10 German 4-cylinder sedan models (listed in the table below) to be compared to the American car statistics. I would like to see if there is a significant difference, in either direction, between German sedans and American sedans. The US Environmental Protection Agency reported that the average MPG for American sedans in 2017 is
??
= 30.6. I set the significance level at α = .10 for a two-tailed hypothesis test.
Hint: Because we know the population mean for the American cars but not the standard deviation, we cannot conduct a Z test but should perform a one-sample t-test instead.
|
German car model |
MPG |
|
1 |
30 |
|
2 |
29 |
|
3 |
29 |
|
4 |
36 |
|
5 |
33 |
|
6 |
32 |
|
7 |
30 |
|
8 |
35 |
|
9 |
35 |
|
10 |
33 |
a. Information about the hypothesis test:
- What is the dependent variable in this hypothesis test?
- What is the “sample” for this one-sample t test?
- What is the target population represented by the sample?
- What is the comparison population?
b.What would be the null and alternative hypotheses in both words and symbol notations for my analysis?
c.Calculate the sample mean
d.Estimate the standard deviation of the population from which the sample was drawn(1 point: .5 if process is correct but answer is wrong)
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