MGMT 305 CHAPTER 14a EXERCISES

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CHAPTER 14a EXERCISES
A study was conducted to test the exertion involved in 2 types of exercise (Ergometer
(ERG)
and Treadmill (TM)) and 2 methods of snow removal. Sustained maximum heartrates for
the subjects doing the activities are recorded in the table below.
ERG TM Blower Shovel 205 180 118 177 177 164 120 151 166 167 111 184 152 173 122 161
142 179 151 192 172 205 158 193 191 156 117 164 170 160 123 207 181 175 127 177 154 191
109 174 We wish to analyze this data using a 1-way ANOVA.
1. Before conducting the 1-way ANOVA, use Minitab to test this dataset to see if the
conditions for a 1-way ANOVA are met.
2. What are the hypotheses for a 1-way ANOVA?
3. Below is the ANOVA table computed by Minitab for this 1-way ANOVA of this data.
One-way ANOVA: Heart Rate versus Method
Analysis of Variance
Source
Method
Error
Total DF
3
36

2. 39 Adj SS
19805
10744
30550 Adj MS
6601.7
298.5 F-Value
22.12 P-Value
0.000 Assuming the conditions for a valid 1-way ANOVA are met, interpret the p-value of
this test. 4. Given the results of this test, what is the next step in the 1-way ANOVA testing
process?
1 5. Further output for the 1-way ANOVA is shown below. What conclusion(s) do you draw
from this output? Tukey Pairwise Comparisons
Grouping Information Using the Tukey Method and 95% Confidence
Method
Treadmill
Snow Shovel
Arm-Crank Ergometer
Snow Blower N
10
10
10

3. 10 Mean
178.00
175.00
171.00
123.60 Grouping
A
A
A
B Tukey Simultaneous 95% CIs
Differences of Means for Heart Rate
Snow Shovel - Arm-Crank Er Snow Thrower - Arm-Crank Er Treadmill - Arm-Crank Er
Snow Thrower - Snow Shovel Treadmill - Snow Shovel Treadmill - Snow Thrower
-80 -60 -40 -20 0 20 40 60 80 If an interval does not contain zero, the corresponding means
are significantly different. 6. How can we test the data if we cannot establish that the
samples were drawn (or were reasonably likely to be drawn) from a normal population?
For that, we need a
2 distribution free test. The distribution free equivalent of 1-way ANOVA is called the
Kruskal-Wallis Test. Suppose your data analyst performs a Kruskal-Wallis test of the
above data and reports a p-value of 0.0056. What further information do you need about
this test in order to interpret this p-value? 3