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Confidence Intervals for Population Mean
7. Sampling Distributions & Confidence Intervals: Mean / Confidence Intervals for Population Mean / Problem 3
Problem 3

A sport psychologist measures the change in reaction time (in units of seconds) for 1212 athletes before and after a specialized training program. Negative values indicate a faster reaction time post‑training. The observed sample is: {0.4,0.1,0.2,0.3,0.0,0.1,0.5,0.3,0.2,0.4,0.5,0.6}\left\lbrace–0.4,0.1,–0.2,0.3,0.0,–0.1,0.5,–0.3,0.2,0.4,–0.5,0.6\right\rbrace. Ten bootstrap samples (with the replacement) of size 1212 are drawn, and their means (in ascending order) turn out to be: 0.47,0.32,0.18,0.05,0.08,0.17,0.29,0.41,0.52,0.67–0.47,–0.32,–0.18,–0.05,0.08,0.17,0.29,0.41,0.52,0.67. Using only these ten bootstrap means, construct an 80%80\% confidence interval estimate for the true mean change in reaction time.