(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 for the two-sided alternative. (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.
Consider the following data set. The data were actually collected in pairs, and each row represents a pair.
Group 1: 48.86, 50.60, 51.02, 47.99, 54.20, 50.66, 45.91, 48.79, 47.76, 51.13
Group 2: 48.88, 52.63, 52.55, 50.94, 53.02, 50.66, 47.78, 48.44, 48.92, 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 for the two-sided alternative.
(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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