Researchers studying the acquisition of pronunciation often compare measurements made on the recorded speech of adults and child

ren. One variable of interest is called "voice onset time" (VOT), the length of time between the release of a consonant sound (such as "p") and the beginning of an immediately following vowel (such as the "a" in "pat"). For speakers of English, this short time lag can be heard as a period of breathiness between the consonant and the vowel. Here are the results for some randomly selected 4-year-old children and adults asked to pronounce the word "pat". VOT is measured in milliseconds and can be either positive or negative.
Children: n = 10, mean = 60.67, standard deviation = 39.89

Adults: n = 20, mean = 88.17, standard deviation = 24.74

You are interested in whether there is a difference in the VOT of adults and children, so you plan to test H0:μa−μc=0 against Ha:μa−μc≠0, where μa and μcare the population mean VOT for adults and children, respectively.

A. What additional information would you need to confirm that the conditions for this test have been met?

B. Assuming the conditions have been met, calculate the test statistic and p-value for this test.

C. Interpret the p-value in the context of this study and draw the appropriate conclusion at
α = 0.05.

D. Given your conclusion in part C, which type error, Type I or Type II, is it possible to make? Describe that error in the context of this study.