Let's perform an independent samples t-test: A statistics teacher wants to compare his two classes to see if they performed any differently on the tests he gave that semester. Class A had 25 students with an average score of 70, standard deviation 15. Class B had 20 students with an average score of 74, standard deviation 25. Using alpha 0.05, did these two classes perform differently on the tests?

Steps for Independent Samples t-Test |
---|

1. Define Null and Alternative Hypotheses 2. State Alpha 3. Calculate Degrees of Freedom 4. State Decision Rule 5. Calculate Test Statistic 6. State Results 7. State Conclusion |

Let's begin.

1. Define Null and Alternative Hypotheses

Figure 1. |
---|

2. State Alpha

Alpha = 0.05

3. Calculate Degrees of Freedom

Figure 2. |
---|

4. State Decision Rule

Using an alpha of 0.05 with a two-tailed test with 43 degrees of freedom, we would expect our distribution to look something like this:

Figure 3. |
---|

Use the t-table to look up a two-tailed test with 43 degrees of freedom and an alpha of 0.05. We find a critical value of 2.0167. Thus, our decision rule for this two-tailed test is:

If t is less than -2.0167, or greater than 2.0167, reject the null hypothesis.

5. Calculate Test Statistic

The first step is to calculate the df and SS for each sample:

Figure 4. |
---|

We then use that information to calculate the pooled variance:

Figure 5. |
---|

Finally, we can calculate our t value:

Figure 6. |
---|

6. State Results

t = -0.67

Result: Do not reject the null hypothesis.

7. State Conclusion

There was no significant difference between the test performances of Class A and Class B, t = -0.67, p > 0.05.