A recent study that examined bone strength collected data from cadaveric femurs
ID: 3319821 • Letter: A
Question
A recent study that examined bone strength collected data from cadaveric femurs from subjects in three age groups. The data are below. Does mean bone strength differ for the three age groups? Use a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available.
Young
Middle Age
Elderly
193.6
122.0
123.0
117.0
99.9
112.8
137.5
100.6
125.4
83.5
94.5
83.3
115.6
72.3
99.7
59.0
88.6
84.5
51.2
57.4
78.2
96.7
78.3
Young
Middle Age
Elderly
193.6
122.0
123.0
117.0
99.9
112.8
137.5
100.6
125.4
83.5
94.5
83.3
115.6
72.3
99.7
59.0
88.6
84.5
51.2
57.4
78.2
96.7
78.3
Explanation / Answer
Step 1
null, Ho: µ1 =µ2 =µ3
alternative, H1: mean bone strength differ for the three age groups
Step 2
Degrees of freedom between = k - 1 = 3 - 1 = 2
Degrees of freedom Within = n - k = 23 - 3 = 20
Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.493
Step 3
Grand Mean = G / N = 98.895
SST = ( Xi - GrandMean)^2 = 21047.0895
SS Within = (Xi - Mean of Xi ) ^2 = 10346.0130
SS Between = SST - SS Within = 10701.076
Step 4
Mean Square Between = SS Between / df Between = 5350.538
Mean Square Within = SS Within / df Within = 517.3006
Step 5
F Cal = MS Between / Ms Within = 10.3431
We got |F cal| = 10.3431 & |F Crit| =3.493
MAKE DECISION
Hence Value of |F cal| > |F Crit|and Here We reject Ho
Mean n Std. Dev 125.80 8 30.020 Young 96.33 7 18.899 Middle Age 74.24 8 16.452 Elderly 98.90 23 30.930 Total