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)is ___.
A)1.3
B)1.14
C)1.04
D)1.02
E)1.47

Question

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)is ___.
A)1.3 
B)1.14 
C)1.04 
D)1.02 
E)1.47

Quizplus · Accepted Answer

The sample standard deviation (s) can be calculated using the formula: s = √[Σd²/(n-1)], where d is the difference between the pairs and n is the number of pairs. Using the given data, we can calculate:

d₁ = 9 - 7.5 = 1.5
d₂ = 6 - 4 = 2
d₃ = 8 - 6 = 2
d₄ = 7 - 5.5 = 1.5
d₅ = 10 - 8 = 2

Σd² = 1.5² + 2² + 2² + 1.5² + 2² = 17.5
n = 5

s = √(17.5/4) = 1.14 (rounded to two decimal places)

Therefore, the answer is B, 1.14.

A Researcher Is Conducting a Matched-Pairs Study