Question 310138
20 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. 
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The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); 
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The control group has a mean of 35 (with an estimated population standard deviation of 5). 
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Using the .05 level, what should the experimenter conclude? 
(a) Use the steps of hypothesis testing, 
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Ho: u(ex)-u(ct) = 0
Ha: u(ex)-u(ct) is not equal to zero
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test stat: t = (38-35)/sqrt[9/20 + 25/30] = 2.6482
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p-value = 2*P(t > 2.6482 with df = 48) = 0.0109
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Conclusion:
At the 5% significance level, reject Ho because the p-value
is less than 5%.
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Cheers,
Stan H.
Note: I'll leave the remainder of the problem to you.
 



(b) sketch the distributions involved, and (c) explain your
answer to someone who is familiar with the t test for a single sample but not
with the t test for independent means.