SOLUTION: 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 knowled

Question 310138: 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? (a) Use the steps of
hypothesis testing, (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.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
------------------------------------------------------
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?
(a) Use the steps of hypothesis testing,
---------------------
Ho: u(ex)-u(ct) = 0
Ha: u(ex)-u(ct) is not equal to zero
------------------------------------------
test stat: t = (38-35)/sqrt[9/20 + 25/30] = 2.6482
---
p-value = 2*P(t > 2.6482 with df = 48) = 0.0109
-------------------------------------------------------------
Conclusion:
At the 5% significance level, reject Ho because the p-value
is less than 5%.
==================================
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.

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