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

Question

Does delaying oral practice hinder learning a foreign language? Researchers randomly assigned 29 beginning students of Russian to begin speaking practice immediately and another 29 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(32, 9) 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? (Round your answers for s to two decimal places.) What is the sampling distribution of the mean score y in the delayed speaking group?

(b) If the experiment were repeated many times, what would be the sampling distribution of the difference y - x between the mean scores in the two groups? (Round your answer for s to two decimal places.)

(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

a) sampling distribution of the mean score x according to central limit theorum would be normal with mean =32

and std error =std deviation/(n)1/2=(9/29)1/2=0.557

sampling distribution of the mean score x according to central limit theorum would be normal with mean =29

and std error =std deviation/(n)1/2=(5/29)1/2=0.415

b)ampling distribution of the difference y - x between the mean scores in the two groups would be normal with mean =32-29=3 and std error =(0.5572+0.4152)1/2=0.6948

c) P(y-x<0)=P(Z<(0-3)/0.6948)=P(Z<-4.3177)=0.0000

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