Matched or Paired Samples · Exercise 35

Lesley E. Tan investigated the relationship between left-handedness vs. right-handedness and motor competence in preschool children. Random samples of 41 left-handed preschool children and 41 right-handed preschool children were given several tests of motor skills to determine if there is evidence of a difference between the children based on this experiment. The experiment produced the means and standard deviations shown. Determine the appropriate test and best distribution to use for that test.

$$\begin{array}{ccc}& \text{Left-handed}& \text{Right-handed}\\ \text{Sample size}& \text{41}& \text{41}\\ \text{Sample mean}& \text{97.5}& \text{98.1}\\ \text{Sample standard deviation}& \text{17.5}& \text{19.2}\end{array}$$

(a) Two independent means, normal distribution
(b) Two independent means, Student’s-t distribution
(c) Matched or paired samples, Student’s-t distribution
(d) Two population proportions, normal distribution

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §10.4 Matched or Paired Samples · Exercise 35