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

Question

Does delaying oral practice hinder learning a foreign language? Researchers randomly assigned 17 beginning students of Russian to begin speaking practice immediately and another 17to 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(29, 9) distribution and scores for delayed speaking have the N(24, 7) 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

in N( ,2 ) =mean and 2 =variance

from above

a)sampling distribution of the mean score x in the early speaking group

mean =29

s=std deviation/(n)1/2 =(9/17)1/2 =0.7276

sampling distribution of the mean score y in the delayed speaking group

mean =24

s=std deviation/(n)1/2 =(7/17)1/2 =0.6417

b)sampling distribution of the difference y - x between the mean scores

mean =24-29 =-5

s=(s12+s22)1/2 =0.9701

c)robability that the experiment will find (misleadingly) that the mean score for delayed speaking is at least as large as that for early speaking =P(Y-X>0)= P(Z>(0-(-5)/0.9701)=P(Z>5.1539) =0.0000

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