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About this document
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- 6 pages
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- $6 one-time, yours to keep
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- Format
- Subject
- Mathematics, Statistics
- Module
- 3 · Week 1
This document explains how to construct a confidence interval and perform a paired t-test for two quantitative variables collected in pairs. It includes an overview of paired data designs and a formula card. It is Module 3, Week 1.
What's inside
- Objectives of the module
- Overview of paired data designs
- Formula card for paired t-tests
- Activity: Comparing book prices at Borders and Amazon
- Steps to perform a paired t-test
- Example exam question on paired t-test
Who it is for: For students studying statistics, particularly those taking a course on statistical methods or hypothesis testing. (Undergraduate)
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Summary
Paired t-tests are used to compare two quantitative variables collected in pairs. Students learn how to construct confidence intervals and perform hypothesis testing for the population mean difference.
Paired data designs
Matched or paired data comes from deliberate experimental designs. Examples include measuring responses before and after a treatment, or comparing matched pairs. Paired designs can involve measurements on the same individual or matched individuals.
Paired t-test procedure
The paired t-test procedure involves stating hypotheses, checking assumptions, computing the test statistic, calculating the p-value, making a decision, and stating a conclusion. The test statistic's distribution is considered if the null hypothesis is true.
Example of a paired t-test
Students are asked to perform a paired t-test to compare book prices from Borders and Amazon. They need to compute the differences in prices and conduct the appropriate hypothesis test. The example guides students through the steps of the paired t-test procedure.
Exam question on paired t-test
An example exam question involves testing the hypothesis of no difference between the utilization of two rooms in a sports facility. Students are given data and SPSS output to interpret the test statistic, state hypotheses, report the p-value, and make a decision.
Key terms
- Paired data
- Data collected in pairs, either from the same individual or matched individuals.
- Confidence interval
- A range of values that estimates the population mean difference with a certain level of confidence.
- Hypothesis testing
- A statistical method to test assumptions about a population parameter.
- Population mean difference
- The average difference between two paired quantitative variables in a population.
- Test statistic
- A value calculated from the sample data to test the null hypothesis.
- P-value
- The probability of observing the test statistic, or something more extreme, if the null hypothesis is true.
Questions this document helps with
- How do you construct a confidence interval for paired data?
- What are the steps in performing a paired t-test?
- How do you interpret the p-value in a paired t-test?
Summary written with AI from the document's text.
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