Does delaying oral practice hinder learning a foreign language? Researchers rand

Question

Does delaying oral practice hinder learning a foreign language? Researchers randomly assigned 18 beginning students of Russian to begin speaking practice immediately and another 18 to delay speaking for 4 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(34, 8) distribution and scores for delayed speaking have the N(32, 3) distribution.

(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? (Round your answer to four decimal places.)

Explanation / Answer

here let x is score of early speaking and y is score of delayed score.

mean score of differnce w =(Xbar -Ybar) =34-32 =2

and std error of mean =(82/18+32/18)1/2 =2.1635

threfore probability that the experiment will find   that the mean score for delayed speaking is at least as large as that for early speaking =P(W<0) =P(Z<(0-2)/2.1635)=(Z<-0.9245)=0.1776

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