A researcher is conducting a matched?pairs study.She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population.The sample standard deviation (s_d)of the differences is _______. A) 1.3 B) 1.14 C) 1.04 D) 1.02 E) 1.47

Question

Quizplus · Accepted Answer

The sample standard deviation of the differences can be calculated by taking the square root of the variance of the differences. The variance of the differences can be calculated by taking the sum of the squared differences, dividing by the sample size minus 1, and then taking the square root. Using the given data, we get:

(7-5.5)^2 + (8.2-7.6)^2 + (6.9-6.2)^2 + (7.4-6.8)^2 + (9.5-8.7)^2 = 10.36
10.36 / (5-1) = 2.59
sqrt(2.59) = 1.14

Therefore, the sample standard deviation of the differences is 1.14 (Choice B).

A Researcher Is Conducting a Matched?pairs Study