The federal government awarded grants to the agricultural departments of 6 universities to test the yield capacities of two new varieties of wheat.

Each variety was planted on a plot of equal area and similar soil conditions at each university, and the yeilds, in kilograms per plot, were recorded as follows:

University Variety 1 Variety 1 #1 38 45 #2 23 25 #3 35 31 #4 41 38 #5 44 50 #6 29 33

Find a 90% confidence interval for the mean difference between the yields of the two varieties, assuming the differences of yields to be approximately normally distributed. Explain why you used the method that you use, i. e., explain why you chose to treat it as a 2 sample problem or a pairing problem.