A sample of n=36 freshmen was selected to participate in a new4-hour training pr

Question

A sample of n=36 freshmen was selected to participate in a new4-hour training program designed to improve study skills. Toevaluate the effectiveness of the new program, the sample wascompared with the rest of the freshman class. All freshmenmust take the same english language skills course, and the meanscore on the final exam for the entire freshman class wasu=74. The students in the new program had a mean score ofM=79.4 with a standard deviation of s=18.
A. On the basis of these data, can the college conclude thatthe students in the new program performed significantly better thanthe rest of the freshman class? Use a one-tailed test witha=.05.

B. Can the college conclude that the students in the newprogram are significantly different from the rest of the freshmanclass? Use a two-tailed test with a=.05.

Explanation / Answer

Given n=36, =74, xbar=79.4 (new program), s=18 (a) For one-tail test with =0.05, Z(0.05)=1.645 (check normaltable). The test hypothesis is Ho:< = 74 Ha:>74 The test statistic is Z=(xbar - )/(s/n) =(79.4-74)/(18/sqrt(36)) =1.8 Since Z=1.8>1.645, we reject Ho. Thus, we can conclude that thestudents in the new program performed significantly better than therest of the freshman class. (b) For two-sided test with =0.05, Z(0.025)=1.96 (checknormal table). The test hypothesis is Ho:=74 Ha: not equal 74 The test statistics is Z=1.8 Since Z=1.8

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