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Conducting a 5-step Hypothesis Testing

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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 5 steps of hypothesis testing listed below, what should the experimenter conclude?

Step 1 (Restate the Question as a research hypothesis and null hypothesis about the populations)

Population 1:
Population 2:
Research Hypothesis
Null Hypothesis

Step 2 (Determine the characteristics of the comparison distribution)
Estimated population variance for population 1
Estimated population variance for population 2
Pooled estimate of the population variance
Variance of distribution of means for population 1
Variance of distribution of means for population 2
Variance of distribution of differences between means
SD of distribution of differences between means

Step 3 (Using the .05 level, determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected)
Probability
Type of test (one or two tailed)
Degrees of freedom total
Cutoff score

Step 4 (Determine your sample's score on the comparison distribution)
t score:

Step 5 (Decide whether to reject the null hypothesis).

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Solution Summary

The solution gives detailed steps on performing a 5-step hypothesis testing. All formula and calculations are shown and explained.

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Solution:
Step 1 (Restate the Question as a research hypothesis and null hypothesis about the populations)
Population 1: all people in the experimental group
Population 2: all people in the control group
Research Hypothesis: µ1 ≠ µ2
Null Hypothesis: µ1 = µ2

Step 2 (Determine the characteristics of the comparison distribution)
Estimated population variance for population ...

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