Statistics for Business: Decision Making and Analysis, 3rd Edition

Chapter Summary

The sampling distribution of the mean of a sample of n items describes the variation among averages from sample to sample. When the sample size condition is satisfied, the sampling distribution of the mean can be modeled as a normal distribution, $\overline{X}~N\left(\mu ,{\sigma }^2/n\right).$ The standard error of the mean is the standard deviation of the sampling distribution, $\text{SE}\left(\overline{X}\right)=\sigma /\sqrt{n}.$ A Type I error occurs when we take unnecessary action (halting production when all is fine); a Type II error occurs when we fail to take appropriate action to remedy a problem (not stopping a faulty production process). The upper and lower control limits determine the probability of a Type I error, denoted by α. An X-bar chart monitors averages of samples. An S-chart monitors ...