Do wearing custom-made shoes, made specifically for the runner, help a runner run faster? To answer this question, twelve competitive runners were randomly selected and their maximum velocity (in mph) was recorded while wearing the custom-made shoes and then again while not wearing the custom-made shoe. (A time for rest was granted and it was randomly determined if they ran with the custom-made shoes first or second. The runners ran 100 yards.) Custom shoes 23.2 20 17.6 22.9 21.5 23 20.8 18.9 | 24 18.8 19.2 19.3 Regular shoes 14.8 16.1 15.4 18 20.4 18.2 19.3 16.3 19 19.6 18.4 | 18.5 a. At the 5% significance level, what conclusion can be reached? b. Are the samples independent or dependent? c. Ifindependent, would using dependent samples have been better? Why or Why not? If depen- dent, explain why dependent samples were used.

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### Do custom-made shoes help a runner run faster?

To answer this question, twelve competitive runners were randomly selected and their maximum velocity (in mph) was recorded while wearing the custom-made shoes and then again while not wearing the custom-made shoe. (A time for rest was granted and it was randomly determined if they ran with the custom-made shoes first or second. The runners ran 100 yards.)

| Custom Shoes | Regular Shoes |
|:------------:|:-------------:|
| 23.2         | 20.0          |
| 14.8         | 16.1          |
| 17.6         | 17.6          |
| 22.9         | 15.4          |
| 21.5         | 20.4          |
| 23.0         | 18.2          |
| 23           | 19.3          |
| 20.8         | 16.3          |
| 18.9         | 19.0          |
| 19.2         | 18.4          |
| 19.3         | 18.5          |
| 18.8         | 19.6          |

#### Analysis Questions:
a. At the 5% significance level, what conclusion can be reached?

b. Are the samples independent or dependent?

c. If independent, would using dependent samples have been better? Why or why not? If dependent, explain why dependent samples were used.
Transcribed Image Text:### Do custom-made shoes help a runner run faster? To answer this question, twelve competitive runners were randomly selected and their maximum velocity (in mph) was recorded while wearing the custom-made shoes and then again while not wearing the custom-made shoe. (A time for rest was granted and it was randomly determined if they ran with the custom-made shoes first or second. The runners ran 100 yards.) | Custom Shoes | Regular Shoes | |:------------:|:-------------:| | 23.2 | 20.0 | | 14.8 | 16.1 | | 17.6 | 17.6 | | 22.9 | 15.4 | | 21.5 | 20.4 | | 23.0 | 18.2 | | 23 | 19.3 | | 20.8 | 16.3 | | 18.9 | 19.0 | | 19.2 | 18.4 | | 19.3 | 18.5 | | 18.8 | 19.6 | #### Analysis Questions: a. At the 5% significance level, what conclusion can be reached? b. Are the samples independent or dependent? c. If independent, would using dependent samples have been better? Why or why not? If dependent, explain why dependent samples were used.
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