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Loss of calcium is a serious problem for older women. To investigate the amount

ID: 3022677 • Letter: L

Question

Loss of calcium is a serious problem for older women. To investigate the amount of loss, a researcher measured the initial amount of bone mineral content in the radius bone of the dominant hand of elderly women and then the amount remaining after one year. The differences, representing the loss of bone mineral content, are given in the following table (courtesy of E. Smith).

8

7

13

3

6

4

8

6

3

4

2

1

11

7

1

8

6

12

13

10

9

11

3

2

9

7

1

16

3

2

10

15

2

5

8

17

8

2

5

5

Round your answers to 3 decimal places.

8

7

13

3

6

4

8

6

3

4

2

1

11

7

1

8

6

12

13

10

9

11

3

2

9

7

1

16

3

2

10

15

2

5

8

17

8

2

5

5

Explanation / Answer

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    273      
As n =    40      
Thus,          
X =    6.825   [ANSWER, MEAN]

******************************  
          
Setting up tables,          
x   x - X   (x - X)^2  
8   1.175   1.380625  
4   -2.825   7.980625  
2   -4.825   23.280625  
8   1.175   1.380625  
9   2.175   4.730625  
7   0.175   0.030625  
10   3.175   10.080625  
17   10.175   103.530625  
7   0.175   0.030625  
8   1.175   1.380625  
1   -5.825   33.930625  
6   -0.825   0.680625  
11   4.175   17.430625  
1   -5.825   33.930625  
15   8.175   66.830625  
8   1.175   1.380625  
13   6.175   38.130625  
6   -0.825   0.680625  
11   4.175   17.430625  
12   5.175   26.780625  
3   -3.825   14.630625  
16   9.175   84.180625  
2   -4.825   23.280625  
2   -4.825   23.280625  
3   -3.825   14.630625  
3   -3.825   14.630625  
7   0.175   0.030625  
13   6.175   38.130625  
2   -4.825   23.280625  
3   -3.825   14.630625  
5   -1.825   3.330625  
5   -1.825   3.330625  
6   -0.825   0.680625  
4   -2.825   7.980625  
1   -5.825   33.930625  
10   3.175   10.080625  
9   2.175   4.730625  
2   -4.825   23.280625  
8   1.175   1.380625  
5   -1.825   3.330625  
          
          
Thus, Sum(x - X)^2 =    733.775      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    40      
          
s^2 =    18.81474359      
          
Thus,          
          
s =    4.337596522   [ANSWER, STANDARD DEVIATION]