Section 11.3 Sample Problems Pages 610 - 611
8. Sodium Contents of Foods The amount of sodium (in milligrams) in one serving for a
random sample of three different kinds of foods is listed here. At the 0.05 level of significance, is
there sufficient evidence to conclude that a difference in mean sodium amounts exists among
condiments, cereals, and desserts?
From Stat Crunch
var1 var2 var3
270 260 100
130 220 180
230 290 250
180 290 250
80
200 300
70
320 360
200 140 300
160
Analysis of Variance results:
Data stored in separate columns.
Column means
Column n
Mean
Std. Dev. Std. Error
var1
7 165.71428 75.466805
var2
7 245.71428 62.678318 23.690178
var3
8
237.5
28.52377
85.64878 30.281418
Section 11.3 Sample Problems Pages 610 - 611
ANOVA table
Source
Treatments
df
SS
MS
F-Stat
2 27543.506 13771.753 2.3985376
Error
19 109092.86 5741.7295
Total
21 136636.36
P-value
0.1178
P Value = 0.1178 > alpha = 0.05
Therefore Do NOT Reject the Null Hypothesis, there is not enough evidence to support the claim that at
least one of the means differs from the others.
Section 11.3 Sample Problems Pages 610 - 611
10. Healthy Eating Americans appear to be eating healthier. Between 1970 and 2007 the per
capita consumption of broccoli increased 1000% from 0.5 to 5.5 pounds. A nutritionist followed
a group of people randomly assigned to one of three groups and noted their monthly broccoli
intake (in pounds). At α = 0.05, is there a difference in means?
Data in Stat Crunch
ar1
var2 var3
2
2
3.7
1.5
1.5
2.5
0.75 4
4
1
3
5.1
1.3
2.5
3.8
3
2
2.9
Analysis of Variance results:
Data stored in separate columns.
Column means
Column n
Mean
Std. Dev. Std. Error
var1
6 1.5916667 0.8126602 0.33176714
var2
6
var3
6 3.6666667 0.9092121
2.5 0.8944272 0.36514837
0.3711843
Section 11.3 Sample Problems Pages 610 - 611
ANOVA table
Source
Treatments
df
SS
MS
F-Stat
2 12.983611 6.4918056 8.515394
Error
15 11.435416 0.7623611
Total
17 24.419027
P-value
0.0034
P Value = 0.0034 <= alpha = 0.05
Therefore Reject the Null Hypothesis, there is enough evidence to support the claim that at least one of
the means differs from the others.
Section 11.3 Sample Problems Pages 610 - 611
14. Cell Phone Bills The average local cell phone monthly bill is $50.07. A random sample of
monthly bills from three different providers is listed below. At α = 0.05, is there a difference in
mean bill amounts among providers?
Data in Stat Crunch
var1
var2
var3
48.2
105.02 59.27
60.59 85.73
65.25
72.5
61.95
70.27
55.62 75.69
42.19
89.47 82.11
52.34
Analysis of Variance results:
Data stored in separate columns.
Column means
Column n Mean Std. Dev. Std. Error
var1
5 65.276
16.15799
7.226073
var2
5
var3
5 57.864 11.029818 4.9326844
82.1 15.697245 7.0200214
Section 11.3 Sample Problems Pages 610 - 611
ANOVA table
Source
Treatments
df
SS
2 1542.2806
Error
12
Total
14 4058.8447
MS
F-Stat
771.1403 3.6771104
P-value
0.0568
2516.564 209.71367
P Value = 0.0568 > alpha = 0.05
Therefore Do NOT Reject the Null Hypothesis, there is not enough evidence to support the claim that at
least one of the means differs from the others.