The following data represent the breaking strengths of samples of 20 gauge insul
ID: 3054561 • Letter: T
Question
The following data represent the breaking strengths of samples of 20 gauge insulated copper wire from three different suppliers. The researcher is interested in finding evidence that the distribution of breaking strength differs by supplier. Use the .01 significance level and the Kruskal-Wallis test to answer the following questions.
Supplier
A
B
C
150
157
143
154
161
147
156
163
151
161
166
154
162
170
156
Give the value of the Kruskal-Wallis test statistic for the above data.
What's the p-value?
What's the critical value?
What's the decision?
What's the expected rank sum for column A if the null hypothesis of identical distributions is true?
Supplier
A
B
C
150
157
143
154
161
147
156
163
151
161
166
154
162
170
156
Explanation / Answer
The following data represent the breaking strengths of samples of 20 gauge insulated copper wire from three different suppliers. The researcher is interested in finding evidence that the distribution of breaking strength differs by supplier.
Here we have to test the hypothesis that,
H0 : the distribution of breaking strength is same by supplier.
H1 : the distribution of breaking strength is different by supplier.
Assume alpha = level of significance = 0.01
Kruskal wallis test we can do in XLSTAT.
steps :
ENTER data into XL sheet --> Non parametric tests --> Comparison of k-samples --> Samples : Select all the data range --> Data format : One column per sample --> Column labels --> Kruskal-Wallis test --> Options -->Significance level : 1 --> ok
Test statistic = 8.692
Critical value = 9.210
P-value = 0.013
P-value > alpha
Accpet H0 at 1% level of significance.
Conclusion : the distribution of breaking strength is same by supplier.
Summary statistics: Variable Observations Obs. with missing data Obs. without missing data Minimum Maximum Mean Std. deviation A 5 0 5 150.000 162.000 156.600 4.980 B 5 0 5 157.000 170.000 163.400 4.930 C 5 0 5 143.000 156.000 150.200 5.263 Kruskal-Wallis test / Two-tailed test: K (Observed value) 8.692 K (Critical value) 9.210 DF 2 p-value (one-tailed) 0.013 alpha 0.01 An approximation has been used to compute the p-value. Test interpretation: H0: The samples come from the same population. Ha: The samples do not come from the same population. As the computed p-value is greater than the significance level alpha=0.01, one cannot reject the null hypothesis H0. The risk to reject the null hypothesis H0 while it is true is 1.30%. Ties have been detected in the data and the appropriate corrections have been applied.Related Questions
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