Calculation practice: Mann–Whitney U-test. Recycling paper has some obvious benefits, but it may have unintended consequences. For example, perhaps people are less careful about how much paper they use if they know that their waste will be recycled. Catlin and Wang (2013) tested this idea by measuring paper use in two groups of experimental participants. Each person was placed in a room alone with scissors, paper, and a trash can, and was told that he or she was testing the scissors. In the “recycling” group only, there was also a recycling bin in the room. The amount of paper used by each participant was measured in grams. The data from each person are listed below.

a. Make and examine histograms of these data. Are the frequency distributions of paper use in the two treatment groups similar in shape and spread?

b. Based on your results in part (a), discuss your options for testing a difference between these two groups in the amount of paper used.

c. We will apply a Mann–Whitney U-test to test the hypothesis that these two treatments have the same distribution of paper use. State the null and alternative hypotheses clearly.

d. Rank all the values of paper use from smallest to largest. Properly account for ties.

e. For each treatment group, calculate the rank sum and the sample size.

f. Calculate the Mann–Whitney U₁ value for the treatment without the recycling bin.

g. Using the result from part (f), calculate U₂ for the treatment with the recycling bin.

h. What is the value of the test statistic U?

i. Calculate the P-value as accurately as you can, state the conclusion of the test, and interpret the results.

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No recycling bin: 4,4, 4,4, 4.4, 4.4, 4.4, 4,4, 4,4, 5,5, 8,8, 9,9, 9,9, 9,9, 9,9, 12.12, 12,12, 13,13, 14,14, 14,14, 14.14, 14,14, 15,15, 2323 With recycling bin: 4,4, 5,5, 8,8, 8,8, 8,8, 9,9, 9,9, 9,9, 12,12, 14,14, 14,14, 15,15, 16,16, 19,19, 23,23, 28,28, 40,40, 43,43, 129,129, 130130