An educator is considering two different videotapes for use in a half-day session designed to introduce students to the basics of economics. Students have been randomly assigned to two groups, and they all take the same written examination after viewing the videotape. The scores are summarized here. Assuming normal populations with equal standard deviations, does it appear that the two videotapes cold be equally effective? What is the most accurate statement that could be made about the p-value for the test?

Question

An educator is considering two different videotapes for use in a half-day session designed to introduce students to the basics of economics. Students have been randomly assigned to two groups, and they all take the same written examination after viewing the videotape. The scores are summarized here. Assuming normal populations with equal standard deviations, does it appear that the two videotapes cold be equally effective? What is the most accurate statement that could be made about the p-value for the test?
Videotape 1: ¯x1 = 77.1 s1 = 7.8 n1 = 25
Videotape 2: x¯2 = 80.0 s2 = 8.1 n2 = 25

MathMate · Answer

First make a hypothesis, for example,
H : the two tapes are equally effective, or
H : &mu₁ = &mu₂
From the given data, calculate the t-statistic
t = (x̄2 - x̄1)/sqrt(s1²/n1+s2²/n2)
Calculate the degrees of freedom:
dof = ((s1²/n1) + (s2²/n2))²/((s1²/n1)²/n1 + (s2²/n2)²/n2)
Look up the Student's t-test values for the corresponding probability that they are equally effective. Use the two-tail test if there is no presumed domininance of one tape over the other.

A detailed numerical example is given in the following link:
http://www.jiskha.com/display.cgi?id=1249353992