Question: Researchers studying the learning of speech often compare measurements made on the recorded speech of adults and children. One variable of interest is called the voice onset time (VOT). Here are the results for 6-year-old children and adults who were asked to pronounce the word “bees.” The VOT is measured in milliseconds and can be either positive or negative.

a. What is the standard error of the sample mean VOT for the 20 adult subjects?

b. What is the standard error of the sample mean VOT for the 10 child subjects.

c. What is the standard error of the difference \({{\bar{X}}_{1}}-{{\bar{X}}_{2}}\) between the mean VOT for children and adults?

d. The researchers were investigating whether VOT distinguishes adults from children. State the appropriate hypotheses and carry out a two-sample t test. Provide an interpretation of your results in a few sentences.