The accompanying data refers to concentration of the radioactive isotope stronti

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.

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: no i's are equalH0: 1 = 2 = 3 = 4
Ha: at least two of the i's are different    H0: 1 2 3 4
Ha: at least two of the i's are equalH0: 1 2 3 4
Ha: all i's are equal

Calculate the test statistic. (Round your answer to two decimal places.)
k =  

What can be said about the P-value for the test?

P-value > 0.1000.050 < P-value < 0.100    0.010 < P-value < 0.0500.001 < P-value < 0.010P-value < 0.001

State the conclusion in the problem context.

Reject H0. There is no evidence that the true average strontium-90 concentration differs for at least two of the regions.Reject H0. There is evidence that the true average strontium-90 concentration differs for at least two of the regions.    Fail to reject H0. There is no evidence that the true average strontium-90 concentration differs for at least two of the regions.Fail to reject H0. There is evidence that the true average strontium-90 concentration differs for at least two of the regions.

Region     1   
2   
3   
4   6.3
7.2
5.7
9.7 5.8
9.9
6.0
12.1 6.4
11.0
8.2
10.3 7.5
10.7
6.7
12.3 5.9
8.7
5.0
11.8

Explanation / Answer

APPLYING ONE WAY anova ON ABOVE data

from above:

H0: 1 = 2 = 3 = 4

Ha: at least two of the i's are different    H0: 1 2 3 4

test statistic F=20.54

P-value < 0.001

Reject H0. There is evidence that the true average strontium-90 concentration differs for at least two of the regions

Groups Count Sum Average Variance 1st 5 31.9 6.38 0.457 2nd 5 47.5 9.5 2.445 3rd 5 31.6 6.32 1.477 4th 5 56.2 11.24 1.358 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 88.38 3 29.46 20.54035 9.83E-06 3.238872 Within Groups 22.948 16 1.43425 Total 111.328 19

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