In Order to Examine the Differences in Age of Teachers $\text { Ages of teachers am ong five school districts }$

question 11

Essay

In order to examine the differences in age of teachers among five school districts, an educational statistician took random samples of six teachers' ages in each district. The data are listed below. $\text { Ages of teachers am ong five school districts }$
$\begin{array} { | c | c | c | c | c | } \hline 1 & 2 & 3 & 4 & 5 \\\hline 42 & 23 & 45 & 31 & 37 \\\hline 22 & 52 & 48 & 45 & 40 \\\hline 33 & 32 & 50 & 33 & 45 \\\hline 32 & 44 & 45 & 38 & 61 \\\hline 26 & 39 & 37 & 29 & 50 \\\hline 24 & 33 & 49 & 46 & 50 \\\hline\end{array}$ Assume that ages of teachers are normally distributed.
Test at the 5% significance level to determine whether differences in teachers' ages exist among the five districts.

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Definitions:

Control Limits

Control limits are the boundaries set in statistical process control that indicate the acceptable range of variation for a process, distinguishing between common and special causes of variation.

Control Charts

Statistical tools used in quality control to monitor, control, and improve the process performance over time by plotting data points in time order.

Lower Control Limit

A statistical measure used in process control, representing the lowest acceptable boundary of process variation for quality assurance.

Upper Control Limit

In quality control, it represents the highest value on a control chart that a process variable can reach before it is considered to signal potential loss of control, necessitating investigation.