Question

answer in the simpilest way



(a)
A track coach is interested in comparing two new types of running shoes, ​Shoe and Shoe , to test whether his runners perform better wearing one ​type of shoe versus the other.

To investigate, the coach recorded the times ​of runners in the -meter dash when wearing Shoe .
He then ​recorded the times for the same runners when wearing Shoe .

The ​runners’ times for the -meter dash wearing each of the two types of ​shoes are shown in the table below.
​
Shoe
A
ATime (s)​ ​11.52 11.75 12.01 11.49 12.46 11.89 12.67 12.42 12.79 11.40 ​ ​Mean Time
=
12.04
=12.04
​Shoe
B
B Time (s) 11.31 11.53 12.04 11.45 12.43 11.42 12.34 11.31 12.53 11.52 ​Mean Time
=
11.79
=11.79

​Part A
What is the difference (Shoe
A
A - Shoe
B
B) in the mean times of the ​runners when wearing Shoe
A
A versus Shoe
B
B ?
​
seconds.

​Part B
The simulation below shows
100
100 results of the differences (Shoe
A
A- ​Shoe
B
B) in the mean times that would be expected if there were no difference in performance when wearing one shoe versus the ​other.

​
​Based on the simulation above and your answer to Part
A
A, is there ​convincing evidence that the runners perform better in the
100
100-meter dash ​when wearing one shoe versus the other? Explain your reasoning.
(b)
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Answer 1

Part A
Difference = mean(A) − mean(B) = 12.04 − 11.79 = 0.25 seconds.

Part B
No. A 0.25 s difference is small and falls within the differences you would commonly see under the “no difference” simulation. Since the observed difference is not unusually large compared with the simulated null distribution, there is not convincing evidence that one shoe gives better performance.