A recent study that examined bone strength collected data from cadaveric femurs
ID: 3396737 • 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. Make sure to 1. give the null and alternative hypotheses, 2. calculate the test statistic, and 3. give the conclusion (including a comparison to alpha or the critical value) to receive full credit.
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
Here we want to compare more than 2 means so one way ANOVA will be used.
1.
Hypothses are:
Ho: Mean bone strength for the three age groups are same.
Ha: Mean bone strength is differ for the at least one of three age groups.
2.
Following is the output of teh ANOVA:
So test statistics is
F=10.343
3.
Degree of freedom of numerator: df1=2
Degree of freedom of denominator: df2=20
So critical value of F for alpha 0.05 is 3.493.
Since F statistics is greater than F-critical so we reject the null hypothesis.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Young 8 1006.4 125.8 901.1857143 Middle Age 7 674.3 96.32857143 357.1557143 Elderly 8 593.9 74.2375 270.6826786 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 10701.07653 2 5350.538265 10.34318872 0.000823777 3.492828477 Within Groups 10346.01304 20 517.3006518 Total 21047.08957 22