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]
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