Question

A taxi company is trying to decide whether the use of radial tires instead of belted tires improves fuel economy. Ten cars were equipped with radial tires and driven over a prescribed course. Without changing drivers, the same cars were then equipped with belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows: | Car | Radial Tires | Belted Tires | | :--- | :--- | :--- | | 1 | 4.8 | 4.6 | | 2 | 5 | 5.4 | | 3 | 6.2 | 5.9 | | 4 | 7.7 | 6.9 | | 5 | 7 | 6.9 | | 6 | 4.3 | 4.5 | | 7 | 6.1 | 5.8 | | 8 | 6.5 | 6.7 | | 9 | 5.2 | 5.7 | | 10 | 4.8 | 4.3 | a) At a 0.01 significance level, can we conclude that cars equipped with radial tires give better (higher) average fuel economy than those equipped with belted tires? Hint: The pairing factor here is the car! Be sure the essential elements of a hypothesis test are clearly identified.

          A taxi company is trying to decide whether the use of radial tires instead of belted tires improves fuel economy. Ten cars were equipped with radial tires and driven over a prescribed course. Without changing drivers, the same cars were then equipped with belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:

| Car | Radial Tires | Belted Tires |
| :--- | :--- | :--- |
| 1 | 4.8 | 4.6 |
| 2 | 5 | 5.4 |
| 3 | 6.2 | 5.9 |
| 4 | 7.7 | 6.9 |
| 5 | 7 | 6.9 |
| 6 | 4.3 | 4.5 |
| 7 | 6.1 | 5.8 |
| 8 | 6.5 | 6.7 |
| 9 | 5.2 | 5.7 |
| 10 | 4.8 | 4.3 |

a) At a 0.01 significance level, can we conclude that cars equipped with radial tires give better (higher) average fuel economy than those equipped with belted tires? Hint: The pairing factor here is the car! Be sure the essential elements of a hypothesis test are clearly identified.

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A taxi company is trying to decide whether the use of radial tires instead of belted tires improves fuel economy. Ten cars were equipped with radial tires and driven over a prescribed course. Without changing drivers, the same cars were then equipped with belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:

| Car | Radial Tires | Belted Tires |
| :— | :— | :— |
| 1 | 4.8 | 4.6 |
| 2 | 5 | 5.4 |
| 3 | 6.2 | 5.9 |
| 4 | 7.7 | 6.9 |
| 5 | 7 | 6.9 |
| 6 | 4.3 | 4.5 |
| 7 | 6.1 | 5.8 |
| 8 | 6.5 | 6.7 |
| 9 | 5.2 | 5.7 |
| 10 | 4.8 | 4.3 |

a) At a 0.01 significance level, can we conclude that cars equipped with radial tires give better (higher) average fuel economy than those equipped with belted tires? Hint: The pairing factor here is the car! Be sure the essential elements of a hypothesis test are clearly identified.

Added by Erik J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ana Carolina Da Cruz

02/04/2024

Step 1

H0: There is no difference in fuel economy between radial tires and belted tires (μ_radial - μ_belted = 0). H1: Cars equipped with radial tires have better fuel economy than those equipped with belted tires (μ_radial - μ_belted > 0). Show more…

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A taxi company is trying to decide whether the use of radial tires instead of belted tires improves fuel economy. Ten cars were equipped with radial tires and driven over a prescribed course. Without changing drivers, the same cars were then equipped with belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows: At a 0.01 significance level, can we conclude that cars equipped with radial tires give better (higher) average fuel economy than those equipped with belted tires? Hint: The pairing factor here is the car! Be sure the essential elements of the hypothesis test are clearly identified.

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Transcript

00:01 So in this question we want to test using a level significance equals to one percent if the cars that are equipped with radial tires have a higher average fuel basically have on average a better fuel economy than those with the other type of tires.

00:26 So so basically what we are testing is if on average those with the radial type has a higher fuel economy than those with the doubted type.

00:42 So that's what we want to test.

00:44 So this is our alternative hypothesis because it does not include the equal sign, which means that our new hypothesis will be the opposite of this claim, which will include the equal sign.

00:55 So to pass this we need to compute the difference between or we can rewrite this to be the difference between the two averages so we can rewrite this to be that these averages less or equal than zero or higher than zero so to pass this considering that we all have a tuple in this case that we have this this pairing factor here, what we're going to do is we're going to compute using the data that we have here, what is the difference between the radial tire with respect to the belted tire.

01:40 So this is the same as computing for each car, 4 .8 minus 4 .6, and we do this until we reach the tenth car which is also 4 .8 minus 4 .3 so in this case what we're gonna get is 0 .2 so this one's 0 .5 but for example car number two we get a difference equals to negative zero four so what we need to do is we need to add these numbers together so we need to have here what is the sum of these differences here to get the average later.

02:21 So the sum of this difference will be in this case equals to 0 .9, which means that the average that we have for the differences here will be 0 .09...

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