t Test Write-up: Matched Pairs Problem Growing Tomatoes

Problem Growing Tomatoes: An agricultural field trial compares the yields of two varieties of tomatoes for commercial use. The researchers divide in half each of 10 small plots of land in different locations and plant each tomato variety on half of each plot. After harvest, they compare the yields in pounds per plant per location. The 10 differences (Variety A-Variety B) give We will now make a 7-step write-up for this problem. This example follows a matched pairs design. We treat the differences as our sample data. Each pair of data points is used to find a difference. This cannot be computed by merely subtracting the means of the two groups. has the higher mean yield at the 5% significance level? Is there convincing evidence that Variety A

Step 1: μ d = (yield of Variety A ) - (yield of Variety B) Step 2: Assumptions: H 0 : μ d = 0 The mean difference in yield between Varieties A and B is zero. H a : μ d > 0 The mean difference in yield between Varieties A and B is positive. We have random assignment to the position in each plot. We are uncertain of meeting the requirement for normal distribution and lack data to analyze.

Step 3: Step 4: df=9

Step 5: P-value = P(t >1.295)= Step 6: p =.11 >.10 + α, so we fail to reject H 0. Step 7: We lack strong evidence of a higher yield for Variety A. While there is some evidence of a higher yield, it was not significant at the 10% level. (We were not able to verify that the population of differences was normally distributed so this is a further concern.)

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