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Two-sample t test versus matched pairs t test. Consider the following data set. The data were actually collected in pairs, and each row represents a pair.
Group 1
Group 2
48.86
48.88
50.60
52.63
51.02
52.55
47.99
50.94
54.20
53.02
50.66
45.91
47.78
48.79
48.44
47.76
48.92
51.13
51.63
(a) Suppose that we ignore the fact that the data were collected in pairs and mistakenly treat this as a two-sample problem. Compute the sample mean and variance for each group. Then compute the two-sample t statistic, degrees of freedom, and P-value.
(b) Now analyze the data in the proper way. Compute the sample mean and variance of the differences. Then compute the t statistic, degrees of freedom, and P-value.
(c) Describe the differences in the two test results.
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