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John wants to test the claim that the mean difference in time to construct a wooden barrel before and after a new "best practices" training is greater than 0 minutes. He selects a random sample of 30 workers and records the time it takes each selected worker to construct a wooden barrel before the training and after the training. Which hypothesis test would be most appropriate for this study? One quantitative sample - sigma known (One Sample Z) One quantitative sample - sigma unknown (One Sample t) Two dependent quantitative samples (Paired Data t) Two independent quantitative samples (Independent Samples t) Three of more quantitative samples (ANOVA) Correlation of two quantitative variables (Linear Regression) Independence of two categorical variables (Chi-Squared)

Ask by Ramirez Chan. in the United States
Feb 19,2025

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The appropriate test is the Paired Data t-test.

Solución

The most appropriate test is the Two Dependent Quantitative Samples (Paired Data t) test. Since John is comparing the time taken by the same workers before and after the training, the data are paired. The paired t-test is designed specifically for comparing two means from related groups where the observations are paired, ensuring that the analysis accounts for the dependency between the measurements.

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Bonus Knowledge

In this scenario, John is looking to compare the time taken by the same workers to construct wooden barrels before and after a training regime. Since the samples are dependent (the same workers are measured twice), the most suitable test is the Paired Data t-test. This test accounts for the correlation between the two sets of measurements, allowing accurate analysis of any mean difference. When conducting the test, it’s crucial to check the assumptions: the differences in time should be normally distributed ideally, or the sample size should be large enough to meet the Central Limit Theorem criteria. A misstep here could lead to incorrect conclusions about the effectiveness of the training!

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