# Statistics: What Should the Experimenter Prove?

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 to find the conclusion, (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.

© BrainMass Inc. brainmass.com June 3, 2020, 11:09 pm ad1c9bdddfhttps://brainmass.com/statistics/students-t-test/statistics-what-should-the-experimenter-prove-266159

#### Solution Preview

Please see the attachments for the full solution.

Conclusion: Reject the null hypothesis. The sample provides enough evidence to support the mean score of experimental ...

#### Solution Summary

This solution provides the step by step method required for calculating the test statistic for the population mean with the help of a graph showing the critical region. Formula for the calculations and interpretations of the results are also included. An interactive excel sheet is provided. The user can edit the inputs and obtain the complete results for a new set of data in the future.