The accompanying data refers to concentration of the radioactive isotope stronti
ID: 2929889 • Letter: T
Question
The accompanying data refers to concentration of the radioactive isotope strontium-90 in milk samples obtained from five randomly selected dairies in each of four different regions. Region 1 2 3 4 6.2 7.1 5.5 9.6 5.6 10.1 5.7 12.0 6.6 11.1 8.4 10.5 7.9 10.3 6.8 12.2 6.3 8.7 5.1 11.6 Test at level 0.10 to see whether true average strontium-90 concentration differs for at least two of the regions. State the appropriate null and alternative hypotheses. H0: 1 2 3 4 Ha: all i's are equal H0: 1 2 3 4 Ha: at least two of the i's are equal H0: 1 = 2 = 3 = 4 Ha: no i's are equal H0: 1 = 2 = 3 = 4 Ha: at least two of the i's are different Correct: Your answer is correct. State the rejection region. Round your answer to three decimal places. k . Compute the krusak wallis test statistic value. Round your answer to three decimal places. . k =
Explanation / Answer
H0: 1 = 2 = 3 = 4
Ha: no i's are equal
1
2
3
4
6.2
7.1
5.5
9.6
5.6
10.1
5.7
12
6.6
11.1
8.4
10.5
7.9
10.3
6.8
12.2
6.3
8.7
5.1
11.6
X1=6.52 X2=9.46 X3=6.3 X4=11.18
X=8.365
SSA=5(6.52-(8.365))^2……5(11.18-(8.365))^2=83.9575
SSW=(6.2-(6.52))^2….(11.6-(11.18))^2=24.808
MSA=83.9575/(4-1)=27.9858
MSW=24.808/(20-4)=1.5505
F=17.9858/1.5505=18.05
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
1
5
32.6
6.52
0.727
2
5
47.3
9.46
2.488
3
5
31.5
6.3
1.775
4
5
55.9
11.18
1.212
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
83.9575
3
27.98583333
18.04955391
2.18327E-05
2.461810753
Within Groups
24.808
16
1.5505
Total
108.7655
19
Reject H0 at a=0.1 as F>FCRIT (2.46)
Kruskal Wallis H Test
H=[12/n(n+1)Etj^2/nj]-3(n+1)
H=[12/20(20+1)*31^2/5+67^2/5+26^2/5+86^2/5]-3(20+1)
H=14.269
1
2
3
4
6.2
7.1
5.5
9.6
5.6
10.1
5.7
12
6.6
11.1
8.4
10.5
7.9
10.3
6.8
12.2
6.3
8.7
5.1
11.6
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