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California State University, Monterey Bay *

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1281

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Mathematics

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Nov 24, 2024

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docx

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MATH 1281 Discussion Assignment Unit 4 Paired data is data that arises from measuring one group of individuals at different points in time. For example, we want to study the effect of a new teaching method on students' test scores. A group of students is tested before and after applying the teaching method. The goal is to determine if there is a significant improvement in results. In this scenario, a paired t-test would be an appropriate statistical test. The differences between the pre- and post-test scores are calculated for each student, and the mean and standard deviation of these differences are calculated. The t-statistic will then be calculated and compared to the critical value. Unpaired data is data in which the independent samples form two separate, unrelated groups, where each individual belongs to only one group. For example, a study comparing the effectiveness of two different vaccines in treating an disease. One group of individuals receives vaccine A, while another group receives vaccine B. The data collected for each group will be independent and not directly related to each other In the paired data example for student grade measures, the data set consists of two columns: one for the student grade measure before the new teaching method and one for the measure after the new teaching method. Each row represents data for an individual. The main difference in paired data is that the observations are linked or connected within each pair. In this case, a one-sample t procedure is appropriate because we compare the mean difference between paired observations to an assumed value (eg, zero) To determine if there is a significant change in students' grades. In the unpaired data example comparing the two vaccines, we have two separate data sets: one for the group receiving vaccine A and one for the group receiving vaccine B. Each data set consists of a single column representing the outcome variable (for example, vaccine effectiveness) and multiple rows representing individual observations. In this case, a two-sample t-test is appropriate because we are comparing the means of two independent groups to determine if there is a significant difference in effectiveness between the two vaccines. (Studocu, 2023)

Reference Studocu, (2023). Statistics . https://www.studocu.com/en-us/messages/question/2996526/you- have-learned-about-t-distribution-paired-and-unpaired-data-and-how-it-is-appropriate-to-use

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