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1.A shoe company wants to compare two materials (A and B) for use on the soles o

ID: 3222036 • Letter: 1

Question

1.A shoe company wants to compare two materials (A and B) for use on the soles of boys' shoes. Now, you would expect certain variability among boys - some boys wear out shoes much faster than others. A problem arises if this variability is large. It might completely hide an important difference between the two materials. Suppose we give each randomly selected boy a special pair of shoes with the sole on one shoe made from material A and the other from material B. This procedure produced the data in the table below: (the measured data represents the height of the sole in millimeters.) Is there enough evidence to show that Material B is better than Material A? (12 points)

Boy

Material A

Material B

1

13.2

14.0

2

8.2

8.8

3

10.9

11.2

4

14.3

14.2

5

10.7

11.8

6

6.6

6.4

7

9.5

9.8

8

10.8

11.3

9

8.8

9.3

10

13.3

13.6

Boy

Material A

Material B

1

13.2

14.0

2

8.2

8.8

3

10.9

11.2

4

14.3

14.2

5

10.7

11.8

6

6.6

6.4

7

9.5

9.8

8

10.8

11.3

9

8.8

9.3

10

13.3

13.6

Explanation / Answer

from above as p value is less then 0.05 level we reject that material A and B are of equal height.

And concluide that Material B is better than Material A

Material A Material B difference(d) 13.2 14 0.8 8.2 8.8 0.6 10.9 11.2 0.3 14.3 14.2 -0.1 10.7 11.8 1.1 6.6 6.4 -0.2 9.5 9.8 0.3 10.8 11.3 0.5 8.8 9.3 0.5 13.3 13.6 0.3 mean 0.410 std deviaition 0.3872 std error= std dev/(n)^(1/2) 0.1224 t stat= (d)/std error 3.3489 p value = 0.0037