Exercises 8.83 and 10.73 presented some data collected in a 1993 study by Susan
ID: 3223959 • Letter: E
Question
Exercises 8.83 and 10.73 presented some data collected in a 1993 study by Susan Beckham and
her colleagues. In this study, measurements of anterior compartment pressure (in millimeters
of mercury) were taken for ten healthy runners and ten healthy cyclists. The researchers also
obtained pressure measurements for the runners and cyclists at maximal O2 consumption. The
data summary is given in the accompanying table.
Condition
Runners
Cyclists
Mean
s
Mean
s
Rest
14.5
3.92
11.1
3.98
80% maximal O2
consumption
12.2
3.49
11.5
4.95
Maximal O2
consumption
19.1
16.9
12.2
4.67
a) Is there sufficient evidence to support a claim that the variability of compartment pressure
differs for runners and cyclists who are resting? Use = .05.
b) Is there sufficient evidence to support a claim that the variability in compartment pressure
between runners and cyclists differs at maximal O 2 consumption? Use = .05.
Condition
Runners
Cyclists
Mean
s
Mean
s
Rest
14.5
3.92
11.1
3.98
80% maximal O2
consumption
12.2
3.49
11.5
4.95
Maximal O2
consumption
19.1
16.9
12.2
4.67
Explanation / Answer
Answer:
Exercises 8.83 and 10.73 presented some data collected in a 1993 study by Susan Beckham and
her colleagues. In this study, measurements of anterior compartment pressure (in millimeters
of mercury) were taken for ten healthy runners and ten healthy cyclists. The researchers also
obtained pressure measurements for the runners and cyclists at maximal O2 consumption. The
data summary is given in the accompanying table.
Condition
Runners
Cyclists
Mean
s
Mean
s
Rest
14.5
3.92
11.1
3.98
80% maximal O2
consumption
12.2
3.49
11.5
4.95
Maximal O2
consumption
19.1
16.9
12.2
4.67
a) Is there sufficient evidence to support a claim that the variability of compartment pressure
differs for runners and cyclists who are resting? Use = .05.
F Test for Differences in Two Variances
Data
Level of Significance
0.05
Larger-Variance Sample
Sample Size
10
Sample Variance
15.84
Smaller-Variance Sample
Sample Size
10
Sample Variance
15.37
Intermediate Calculations
F Test Statistic
1.0308
Population 1 Sample Degrees of Freedom
9
Population 2 Sample Degrees of Freedom
9
Two-Tail Test
Upper Critical Value
4.0260
p-Value
0.9646
Do not reject the null hypothesis
Calculated F=1.0308 < critical value 4.026. Ho is not rejected.
There is no sufficient evidence to support a claim that the variability of compartment pressure
differs for runners and cyclists who are resting.
b) Is there sufficient evidence to support a claim that the variability in compartment pressure
between runners and cyclists differs at maximal O 2 consumption? Use = .05.
F Test for Differences in Two Variances
Data
Level of Significance
0.05
Larger-Variance Sample
Sample Size
10
Sample Variance
285.61
Smaller-Variance Sample
Sample Size
10
Sample Variance
21.8089
Intermediate Calculations
F Test Statistic
13.0960
Population 1 Sample Degrees of Freedom
9
Population 2 Sample Degrees of Freedom
9
Two-Tail Test
Upper Critical Value
4.0260
p-Value
0.0007
Reject the null hypothesis
Calculated F=13.096 > critical value 4.026. Ho is rejected.
There is sufficient evidence to support a claim that the variability in compartment pressure
between runners and cyclists differs at maximal O 2 consumption.
Condition
Runners
Cyclists
Mean
s
Mean
s
Rest
14.5
3.92
11.1
3.98
80% maximal O2
consumption
12.2
3.49
11.5
4.95
Maximal O2
consumption
19.1
16.9
12.2
4.67
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