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?
Question- Sketch the distributions involved
To answer this question, we need to compare the distributions of the experimental group and the control group. The mean and standard deviation for each group are provided:
Experimental Group:
Mean (μ1) = 38
Standard deviation (σ1, estimated) = 3
Control Group:
Mean (μ2) = 35
Standard deviation (σ2, estimated) = 5
To sketch the distributions, we can start by drawing a horizontal axis to represent the test scores. Then, we can plot the distribution for the experimental group and the control group separately.
For the experimental group, we would expect a bell-shaped distribution centered around the mean of 38. Since the population standard deviation is estimated to be 3, we can draw the distribution with a spread of approximately 3 standard deviations in each direction from the mean. This can be represented by drawing the distribution curve slightly wider.
For the control group, we would also expect a bell-shaped distribution centered around the mean of 35. Since the population standard deviation is estimated to be 5, we can draw the distribution curve wider compared to the experimental group to account for the larger spread.
Remember, this is just a sketch, so we don't need to be precise. The key is to visualize the distributions and understand that they will overlap to some extent.
Once you have sketched the distributions, you can analyze the data further to draw conclusions about the experiment.