Independent Samples t-Tests

Chapter Objectives
The reader will be able to:
-Understand the use of Independent Samples t Test as a test of two independent sample means
-Understand the role of independent and dependent variables
-Understand the concept of standard error of the difference between means as the average expected difference between two random samples from two different populations on a measurement
-Interpret the results through the probability level that the null -hypothesis is true

Exercise for Chapter 22
Factual Questions

1. What is the scenario when performing an Independent Samples t Test is required?

2. Assume that a researcher interested in growth spurts among young teens decided to measure the height difference between boys and girls in middle school from a random sample of 200 boys and girls. In this study, what are the two variables of interest and which of the two variables is the independent variable and the other, the dependent variables?

3. In the above scenario, state the null and the alternative hypotheses.

4. If alternative hypothesis is as follows: H A: 1 2, and you rejected the null hypothesis in favor of the alternative hypothesis, state in words what you would conclude.

5. The above alternative hypothesis would be (circle one)?
A. Nondirectional hypothesis
B. Directional hypothesis

6. In another study, if the alternative hypothesis is
1 <
2 , and you concluded in favor of the alternative hypothesis, in words what you would conclude?

7. The above alternative hypothesis would be (circle one)?
A. Nondirectional hypothesis
B. Directional hypothesis

8. Generally, the larger the samples, the smaller the standard errors become, increasing the likelihood of finding statistical significance. This statement is (circle one)?
A. True
B. False

9. Calculating the standard error of the difference between means depends on the standard deviations as well as the sample sizes between the groups, and can be considered equal or unequal. This statement is (circle one)?

A. True
B. False
10. What do the following results indicate in terms of rejecting the null hypothesis: (t = 3.20, df = 28, p < .05, two-tailed test)?

Question for Discussion
11. Give an example of one continuous data and one categorical data with two categories that would require performing an Independent Samples t Test.

Notes
1. If the sample sizes or the standard deviations are very different between the two independent groups, one needs to consider nonparametric tests such as the Mann–Whitney U test as an alternative.
2. A full explanation about the degrees of freedom is beyond the scope of this book.
3. Review Chapter 20 on probability.