The U.S. Environmental Protection Agency (EPA) monitors levels of pollutants in
ID: 3134715 • Letter: T
Question
The U.S. Environmental Protection Agency (EPA) monitors levels of pollutants in the air for cities across the country. Ozone pollution levels are measured using a 500-point scale; lower scores indicate little health risk, and higher scores indicate greater health risk. The following data show the peak levels of ozone pollution in four cities (Birmingham, Alabama; Memphis, Tennessee; Little Rock, Arkansas; and Jackson, Mississippi) for 10 dates in 2012 (U.S. EPA website, March 20, 2012).
AL/TN/AR/MS
Jan 9: 18/20/18/14
Ja 17:23/ 31/22/30
Ja 18:19/25/22/21
Ja 31:29/36/28/35
Feb 1:27/31/28/24
Feb6: 26/31/31/25
Fe14:31/24/19/25
Fe17:31/31/28/28
Fe20:33/35/35/34
Fe29:20/42/42/21
***Need to know the SS (3 decimals), df, MS (4 dec), F (4 dec), P value (4 dec), and F crib (4 dec) FOR EACH Row, and column as well as the error of SS, df and MS
The slashes divide each column in the data above.
Explanation / Answer
Randomized Block Design (ANOVA: Two-Factor Without Replication)
SUMMARY
Count
Sum
Average
Variance
j9
4
70
17.5000
6.3333
j17
4
106
26.5000
21.6667
j18
4
87
21.7500
6.2500
j31
4
128
32.0000
16.6667
f1
4
110
27.5000
8.3333
f6
4
113
28.2500
10.2500
f14
4
99
24.7500
24.2500
f17
4
118
29.5000
3.0000
f20
4
137
34.2500
0.9167
f29
4
125
31.2500
154.2500
AL
10
257
25.7000
29.5667
TN
10
306
30.6000
40.7111
AR
10
273
27.3000
55.7889
MS
10
257
25.7000
40.4556
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Rows
903.025
9
100.3361
4.5479
0.0010
2.2501
Columns
160.075
3
53.3583
2.4186
0.0880
2.9604
Error
595.675
27
22.0620
Total
1658.775
39
Level of significance
0.05
For rows, Calculated F=4.5479, P=0.001 which is > 2.2501 table value.
The null hypothesis is rejected.
There is significant difference between the rows.
For columns, Calculated F=2.4186 < 2.9604 table value.
The null hypothesis is not rejected.
There is no significant difference between the columns.
Randomized Block Design (ANOVA: Two-Factor Without Replication)
SUMMARY
Count
Sum
Average
Variance
j9
4
70
17.5000
6.3333
j17
4
106
26.5000
21.6667
j18
4
87
21.7500
6.2500
j31
4
128
32.0000
16.6667
f1
4
110
27.5000
8.3333
f6
4
113
28.2500
10.2500
f14
4
99
24.7500
24.2500
f17
4
118
29.5000
3.0000
f20
4
137
34.2500
0.9167
f29
4
125
31.2500
154.2500
AL
10
257
25.7000
29.5667
TN
10
306
30.6000
40.7111
AR
10
273
27.3000
55.7889
MS
10
257
25.7000
40.4556
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Rows
903.025
9
100.3361
4.5479
0.0010
2.2501
Columns
160.075
3
53.3583
2.4186
0.0880
2.9604
Error
595.675
27
22.0620
Total
1658.775
39
Level of significance
0.05
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