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 meanof 38 on the test (with an estimated population standard deviationof 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the 5 steps of hypothesis testinglisted 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 variancefor 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).

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 …

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