STAT 245 Lecture Notes - Lecture 9: Analysis Of Variance, Oxygen Saturation, Contingency Table
STAT 245 – Exercises #9
Solutions
1. Several water samples were taken at each of four locations of the South Saskatchewan River as it
flows by and through Saskatoon. The quantity of dissolved oxygen, a measure of water pollution,
was determined for each water sample. Based on the results presented below, is there sufficient
evidence to conclude the existence of a difference in mean dissolved oxygen content at the four
locations? Note that: the lower the level of dissolved oxygen, the greater the level of pollution
present.
Location
Observed Dissolved Oxygen Content
A
5.9
6.1
6.4
6.1
6.0
B
6.2
6.4
6.4
6.1
6.3
6.0
C
5.9
5.8
6.0
5.7
5.9
D
6.0
6.4
6.1
5.9
Perform the 8-step ANOVA using a 5% level of significance.
First of all, we expand the table:
Location
Observed Dissolved Oxygen Content
Sum
Size
Mean
Variance
A
5.9
6.1
6.4
6.1
6.0
30.5
5
6.1
0.035
B
6.2
6.4
6.4
6.1
6.3
6.0
37.4
6
6.233333
0.026667
C
5.9
5.8
6.0
5.7
5.9
29.3
5
5.86
0.013
D
6.0
6.4
6.1
5.9
24.4
4
6.1
0.046667
Overall
121.6
20
6.08
1. Hypotheses: vs.
2. Level of Significance:
3. Test Statistic:
4. Calculate TS:
