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Hypotheses for Two-Sample Tests: Independent Samples vs Dependent Samples

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Respond to the following:
- Give two examples as follows:
o A research situation when you would use a two-sample test with independent samples
o A research situation when you would use a two-sample test with dependent samples
- Explain why you would choose the specific test.
- Define the null hypothesis and the alternate hypothesis for the two research situations you developed. Explain the difference between null and alternate hypotheses using the examples.

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Solution Preview

Hypothesis Testing With Two Samples
Respond to the following:
• Give two examples as follows:
o A research situation when you would use a two-sample test with independent samples
A researcher wants to compare the percentage of self-described religious people who support marriage equality in the gay and lesbian communities to the percentage of self-described atheists who support the same thing, in an effort to understand the effect (if any) that religion has in whether someone supports marriage equality, or not. By taking a random sample from within the religious community and a random sample from within the atheist community to create your data set, where those people randomly selected from within one group have no impact, bearing or influence on any of the people randomly selected from the other group, you are taking totally independent random samples.

Explain why you would choose the specific test.
A two-sample test would be appropriate in this case because there are two groups that the researcher wishes to compare: religious people and atheists, and the way that the samples are being collected makes them independent samples.

Define the null hypothesis and the alternate hypothesis for the two research situations you developed.
If the religious community is considered population #1 and the atheist community is considered population #2, then if you are looking for any significant difference between the two groups your hypotheses would be this pair:

Explain the difference between null and alternate hypotheses using the ...

Solution Summary

Specific situations are described where a two-sample, independent test would be appropriate and where a two-sample, dependent test would be appropriate.

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Hypothesis Testing, Statistical Inference, and Regression Analysis

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2. What are the differences between one- and two- sample hypothesis tests? Describe the correct mathematical form for specifying the null and alternative hypotheses for both types of tests.
3. Explain Type I and Type II errors. Which one is controllable by the experimenter?
4. What is the difference between paired and independent samples?
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6. Explain the difference between simple and multiple linear regression.
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