250 W17 Lab7 Mean Difference - Lab 7 Paired Data Analysis...

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Lab Workbook Page 51 Lab 7: Paired Data Analysis Objective:In this lab, you will learn how to perform a hypothesis test in the case when we have two quantitative variables collected in pairs, called a paired t-test. You will make a confidence interval for and test hypotheses about the population mean difference, ʅd. Using these, you will be able to provide a statement about how confident you are regarding your interval estimate or in your decision. Application: Mackenzie believes that college students can run a mile faster in the afternoon then they can in the morning. She has ten of her friends run a mile early in the morning and also late in the afternoon and she records their time in seconds. For each of her ten friends Mackenzie computes a difference: time to run the morning mile (in seconds) – time to run the afternoon mile (in seconds). Runner AM PM Difference (AM – PM) Runner 1 633.8 618.9 14.9 Runner 2 588.9 569.6 19.3 Runner 3 619.4 630.9 -11.5 Runner 4 640.9 628.5 12.4 Runner 5 613.9 574.2 39.7 Runner 6 590.0 627.3 -37.3 Runner 7 613.4 603.3 10.1 Runner 8 568.6 593.1 -24.5 Runner 9 637.0 596.2 40.8 Runner 10 648.6 613.4 35.2 Overview: Matched or paired data results from a deliberate experimental design scheme. Mackenzie’s scenario is one example of a paired design. Another example of a paired design is an experiment where rats are matched by weight, where one rat in each match receives a new diet and the other rat in the match receives a control diet. These types of design are called paired data designs. Note that paired designs can occur when you have two measurements on the same individual OR when you have two individuals that have been matched or paired prior to administering a treatment. The inference procedures for a paired data design are based on the one-sample t-test procedures from the previous lab. The change is that we want to estimate or test hypotheses about the population mean difference ʅd, which is generally compared to a hypothesized value of zero, indicating no difference on average. The assumptions are similar to those assumptions made for the one sample t-test. Going back to the application, Mackenzie now must assume the sample of the ten differences in running time is a random sample. This can be verified by creating a time plot of those ten sample differences and checking for stability. She must also assume that the population of differences is normally distributed. Mackenzie can

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