A nurse at a local hospital wonders if the firstborn twin is taller than the second-born. He randomly selects the medical records of 33 sets of twins and finds the differences open paren firstborn minus second-born close paren in the twins’ heights, in centimeters. The mean of the differences is 1 point 1 centimeters with a standard deviation of 2 point 3 centimeters. Assuming the conditions for inference are met, what is the cap p -value for testing the hypotheses ratio of cap h sub 0 to mu sub diff is equal to 0 ; ratio of cap h sub A to mu sub diff is greater than 0 ? Refer to the t -table.
Use a one-sample t statistic for the mean paired difference: t = (1.1 − 0)/(2.3/√33) ≈ 2.75, with 32 degrees of freedom. Because the alternative is that the mean difference is greater than 0, the P-value is the area to the right of 2.75. From the t-table, this is about 0.0049, so the correct choice is 0.0049.
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