Did labor force participation rates (LFPR) for women increase between 1968 and 1972? The Data and Story Library (DASL) contains LFPR figures for 1968 and 1972, for each of 19 cities. Go to the DASL website (lib.stat.cmu.edu/DASL/) and retrieve the Women in the Labor Force data set (lib.stat.cmu.edu/DASL/ Datafiles/LaborForce.html). Produce appropriate graphical (histogram, stem-and-leaf, box plot) and numerical summaries of the LFPR data and conduct the following nonparametric statistical analyses (data sets: LaborFrc.xIsx, LaborFrc.mtw):
a. Do the data provide sufficient evidence to conclude that the LFPR for women increased between 1968 and 1972? Conduct a nonparametric, two-sample, independent samples Wilcoxon rank sum test at the 0.01 level of significance. Clearly state the hypotheses and your conclusion. Report the p-value (observed level of significance) for your test.
b. Consider, as an alternative to the foregoing independent sample analysis, a paired sample procedure, the nonparametric Wilcoxon signed ranks test. Test once more the hypothesis of part a, this time using the Wilcoxon signed ranks test applied to the differences in LFPRs [1972 1968]. Again, clearly state your conclusion and p-value.
c. Between the two tests of parts a and b, which is the more appropriate for the current data situation? Why?