Last fall, a sample of n=36 freshman was selected to participate in a new 4- hou

Question

Last fall, a sample of n=36 freshman was selected to participate in a new 4- hour training program designed to improve study skills. To evaluate the effectiveness of the program, the sample was compared with the rest of the freshman class. All freshmen must take the same English Language Skills course, and the mean score on the final exam for the entire freshman class was µ=74. The students in the new program had a mean scores of M=79.4 with a standard deviation of s=18.
(a). On a basis of these data, can the college conclude that the students in the new program performed significantly, better that the rest of the freshman class? Us a one- tailed test with ?=.05.
(b). Can the college conclude that the students in the new program are significantly different from the rest of the freshman class? Use a two- tailed test with a ?=.05.

Explanation / Answer

We use a t test because we are using the standard deviation of the sample to conduct the test. The t test statistic is (79.4-74)/(18/sqrt36)= 5.4/3= 1.8 Looking up in a t table (degrees of freedom are 36-1= 35 so we use 30 to be conservative) we get One tailed test .025

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