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 = 0.0037Related Questions
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