refer to the indicated data set in Appendix B and use the Wilcoxon rank-sum test. Weights of Quarters ?Data Set 21 in Appendix B lists weights (g) of pre-1964 quarters and post-1964 quarters. Use a 0.05 significance level to test the claim that the samples are from populations with the same median. Does it appear that the design of quarters changed in 1964?
Solution 11BSC Step 1 : Given, In the above example the data consists weights (g) of pre-1964 and post-1964 quarters.so the observations from the same population. Hence first requirement of the Wilcoxon Rank-Sum test satisfied. Each samples contains 12 values, it satisfies the second condition that the each sample should have the same median. Where Sample 1 = weights of pre-1964 quarters and Sample 2 = weights of Post-1964 quarters Hypothesis : H 0 The median of Pre-1964 quarters weights are equal to the median of Post-1964 quarters weights H : The median of Pre-1964 quarters weights are not equal to the median of Post-1964 1 quarters weights Step 2 : We have 24 observations ,based on the values we give ranks, if it is least value then rank will be 1 and next to the value will be 2 and so on. If there is a tie then mean of the values is the rank, Ranks for sample 1 are 23, 18, 13, 19, 14, 16, 15, 24, 20, 17, 21, 22. The sum of the ranks for sample 1 = 222