Questions and Answers
When can one use the Pooled variance t-test?
One can use this test if the random samples are independently selected from two populations that are normally distributed and have equal variances.
When is the paired t-test for the mean difference used?
This test is used for examining the difference between two populations when data is collected from related populations.
What are the 3 rules or assumptions for the Pooled Variance test?
What is the null hypothesis in testing for differences between the means of two related populations?
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What test should a researcher use if they choose 60 students and give each two tests after different amounts of sleep?
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What are the 3 assumptions for the Paired t-test?
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The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.
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In the professor's situation, he should use a t-test with related samples.
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Study Notes
Pooled Variance t-test
- Applicable when random samples are independently selected from two populations.
- Requires the populations to be normally distributed with equal variances.
Paired t-test for Mean Difference
- Used to examine the difference between two related populations.
- Samples must be related, indicating that the outcomes from the first population affect the second.
Assumptions for Pooled Variance Test
- Equal variances must exist between populations.
- Populations should be normally distributed.
- Each value must be sampled independently.
Null Hypothesis for Related Populations
- The null hypothesis states that the mean difference (D) equals zero (H0: D = 0).
Related Samples Test Example
- A researcher assesses sleep impact on student test performance by testing the same 60 students after two different amounts of sleep.
- The appropriate test in this scenario is a related samples test.
Assumptions for Paired t-test
- Homogeneity of variance is required: both populations should have the same variance.
- The populations must be normally distributed.
- Each measurement must be independent, meaning no subject should contribute more than one score.
Sample Size in Independent Samples
- Sample sizes do not need to be equal across independent populations to test for mean differences.
Misapplication of t-test
- A professor incorrectly uses a related samples t-test when the variances are equal for upper and lower classmen’s grades.
- The correct approach would have been to apply the paired t-test for assessing independent means.
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Description
Test your understanding of key statistical tests covered in BNAL 306 Chapter 10. This quiz focuses on the Pooled variance t-test and the Paired t-test, two essential concepts in comparing population means. Perfect for reinforcing your knowledge before exams!
