Based on the following problem, should I run a 1-tail or a 2-tailindependent sam

Question

Based on the following problem, should I run a 1-tail or a 2-tailindependent sample t-test?

An Air force introductory course in electronics uses a personalizedsystem of instruction whereby each student views a videotapedlecture and then is given a programmed instruction text. Thestudents work independently with the text until they have completedthe training and passed a test. Of concern is the varying pace atwhich the students complete this portion of their training program.Some students are able to cover the programmed instruction textrelatively quickly, whereas other students work much longer withthe text and require additional time to complete the course. Thefast students wait until the slow students complete theintroductory course before the entire group proceeds together withother aspects of their training.

A proposed alternative system involves use of computer-assistedinstruction. In this method, all students view the same videotapedlecture and then each is assigned to a computer terminal forfurther instruction. The computer guides the student, workingindependently, through the self-training portion of the course.

To compare the proposed and current methods of instruction, anentering class of 122 students was assigned randomly to one of thetwo methods. One group of 61 students used the currentprogrammed-text method and the other group of 61 used the proposedcomputer-assisted method. The time in hours was recorded for eachstudent in the study. The data Training in excel is uploaded.

Explanation / Answer

A one tail test. You are comparing the oldand new methods, not the fast and slow students. You want to know if the new method isFASTER than the old method. The nature of the study makes it unlikelyto slow down fast students, so that tail is notrelevant.
In general, the decision of a one- ortwo-tailed t-test is whether the total area of theresult is placed in one tail or divided equally between thethe two tails of normal distribution. The one-tailed t-test isperformed if the results are interesting only if they turn out inone particular direction that you select BEFOREHAND. The two-tailedt-test is performed if the results would be useful in eitherdirection.

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