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Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, what should the experimenter conclude?
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to your Z score.
(a) and (c)
Ho: u(ex) - u(ct) = 0
Ha:u(ex) – u(ct) is not equal to 0
Test stat: t = (38-35) / sqrt[9/20 + 25/30] = 2.6482
p-value = 2*P(t > 2.6482 with df = 48) = 0.0109
At the 5% significance level, reject Ho because the p-value is less than 5%