Answer
The study is to check whether there is dissimilarity between the median length of school-going years of black and white children in the year 1887. The concept of Wilcoxon matched-pairs signed-ranks test is used to check the claim.
The hypotheses are formulated as
\[\begin{align}
& {{H}_{0}}:\ {{M}_{D}}=0 \\
& {{H}_{1}}:\ {{M}_{D}}\ne 0
\end{align}\]
where\[{{M}_{D}}\]symbolizes the median value of the differences of the length of school-going years.
To obtain the result of the test, the stepsgiven below are followed in the Minitab software.
Step 1: Enter the data in Minitab worksheet.
Step 2: Select the “calculator” option under the Calc menu. Specify the column where the result of difference will be stored and specify the function for computing the difference in the “Expression” tab.
Step 3: Go to Stat and select 1-Sample Wilcoxon under nonparametric option.
Step 4: Input the column number of difference in the cell named “Variables.”
Step 5: Click “Test Median” and enter “0” in the cell.
Step 6: Under the option “Alternative,” select “not equal.” Click Ok.
The output shows that the p-value is obtained as \[p=0.000\].
Since the calculated\[p=0.000\] is less than the significance level \[\alpha =0.05\], the null hypothesis is discarded.
It can be decided that there is adequate indication to say that the length of the school-going years is different for white and black children in the year 1887.
The study is to check whether there is dissimilarity between the median length of school-going years of black and white children in the year 1915. The concept of Wilcoxon matched-pairs signed-ranks test is used to check the claim.
The hypotheses are formulated as
\[\begin{align}
& {{H}_{0}}:\ {{M}_{D}}=0 \\
& {{H}_{1}}:\ {{M}_{D}}\ne 0
\end{align}\]
where\[{{M}_{D}}\]symbolizes the median value of the differences of the length of school-going years.
To obtain the result of the test, the stepsgiven below are followed in the Minitab software.
Step 1: Enter the data in Minitab worksheet.
Step 2: Select the “calculator” option under the Calc menu. Specify the column where the result of difference will be stored and specify the function for computing the difference in the “Expression” tab.
Step 3: Go to the Stat and select 1-Sample Wilcoxon under nonparametric option.
Step 4: Input the column number of difference in the cell named “Variables.”
Step 5: Click “Test Median” and enter “0” in the cell.
Step 6: Under the option “Alternative,” select “not equal.” Click Ok.
The output shows that the p-value is obtained as \[p=0.000\].
Since the calculated \[p=0.000\] is less than the significance level \[\alpha =0.05\], the null hypothesis is discarded.
It can be decided that there is adequate indication to say that the length of the school-going years is different for white and black children in the year 1915.
Work Step by Step
Given above.
