Question

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 in Table 10.36. Determine the appropriate test and best distribution to use for that test.

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

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

Short answer

The provided data is two independent means, Student’s-t distribution.

Step-by-step solution

Given Information

Given data:

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

Explanation

Testing can be carried out if the data and mean-variance of both samples are determined, and the population standard deviation is unknown, two independent means, Student's-t distribution.