Does delaying oral practice hinder learning a foreign language? Researchers randomly assigned 25 beginning students of Russian to begin speaking practice immediately and another 25 to delay speaking for four weeks. At the end of the semester both groups took a standard test of comprehension of spoken Russian. Suppose that in the population of all beginning students, the test scores for early speaking vary according to the N(32, 6) distribution and scores for delayed speaking have the N(29, 5) distribution.
(a) What is the sampling distribution of the mean score x in the early-speaking group in many repetitions of the experiment? What is the sampling distribution of the mean score yin the delayed-speaking group?
(b) If the experiment were repeated many times, what would be the sampling distribution of the difference y-xbetween the mean scores in the two groups?
(c) What is the probability that the experiment will find (misleadingly) that the mean score for delayed speaking is at least as large as that for early speaking?