5/26 points 1 Previous Answers B8UnderStat11 My Notes Ask Your Teac The quantity
ID: 3369377 • Letter: 5
Question
5/26 points 1 Previous Answers B8UnderStat11 My Notes Ask Your Teac The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location II was 200 meters above the discharge point and in midstream. Location III was 50 meters downstream from the discharge point and near the shore. Location IV was 200 meters downstrean from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more pollution. Because of the difficulty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use a 1% level of significance. Do we reject or not reject the car that the quantity of dissolved oxygen does not vary from one location to another? Location I :7.2 6.8 7.5 6.9 6.4 Location II 6.3 7.2 7.3 8.0 Location III 4.2 5-6 4.3 Location IV 4.3 (a) What is the level of significance? 0.01 State the null and alternate hypotheses Ho: ?1-P2-P3 Ha; Hi : Exactly three means are equal. O Ho: ??-?2-?3-DG HI : Not all the means are equal. Ho' ? 1-P2 " ?3-Hai Hi: All four means are different. Ho: /11-P2 .. ?3-?4; H 1: Exactly two means are equal.Explanation / Answer
I have done anova in MINITAB.
One-way ANOVA: Location1, Location2, Location3, Location4
Method
Null hypothesis
All means are equal
Alternative hypothesis
Not all means are equal
Significance level
? = 0.01
Rows unused
1
Equal variances were assumed for the analysis.
Factor Information
Factor
Levels
Values
Factor
4
Location1, Location2, Location3, Location4
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Factor
3
17.492
5.8306
11.66
0.001
Error
13
6.499
0.4999
Total
16
23.991
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
0.707034
72.91%
66.66%
51.07%
Means
Factor
N
Mean
StDev
99% CI
Location1
5
6.960
0.416
(6.008, 7.912)
Location2
4
7.200
0.698
(6.135, 8.265)
Location3
5
4.900
0.791
(3.948, 5.852)
Location4
3
5.333
0.961
(4.104, 6.563)
Pooled StDev = 0.707034
In above output we can see that Factor means Between groups and Error means within groups .We also having corresponding degree of freedom . F statistics
Critical value for F statistics=3.54 and calculated value 11.66 reject H0.
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