A recent study that examined bone strength collected data fr

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

Solution

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.