STAT101 Study Guide - Confidence Interval, Point Estimation, Standard Deviation
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Two machines are used to fill glass bottles with a net volume of 13. 0 mi. The filling processes are assumed to be normally distributed, with common but unknown standard deviations. The quality department suspects that both machines fill to the same net volume, whether or not this volume is 13. 0m1. An experiment is performed by taking a random sample from the output of each machine. Construct a 100(1-\alpha)% confidence interval for difference between two means (\mu_1- X_{1} = \begin{bmatrix} 13. 01 & 13. 03 \ 12. 98 & 12. 96 \ 13. 02 & 13. 04 \ 13. 05 & X_{2} = \begin{bmatrix} 13. 01 & 13. 00 \ 12. 97 & 12. 96 \ 13. 04 & 12. 99 \ 13. 01 & Find the confidence interval for the difference between two means (\mu_{1}- Recall that confidence interval is expressed as (point estimate) \pm (margin of error). The margin of error e, derived from this formula, is: t_{(\frac{\alpha}{2}, n_{1}+n_{2}-2)} imes \sqrt{(\frac{s_{1}^{2}}{n_{1}}) + (\frac{s_{2}^{2}}{n_{2}})}. To find point estimate (\bar{x}_{1}-\bar{x}_{2}), calculate \bar{x}_{1} and.
