LAB 3:

In the chapters that follow, we are going to learn how to make inferences about populations based on information in a sample. Several of these techniques are based on the assumption that the population is approximately normally distributed. However, not all continuous distributions are normally distributed. It will be important to determine whether the sample data come from a normal population before we can properly apply these techniques.

Below are 4 different methods to check for normality.

1. Construct a histogram or stem-and-leaf plot for the data and note the shape of the graph. If the data are approximately normal, the shape of the graph will be similar to the normal curve.
2. Compute the intervals \(\bar{x} \pm s, \bar{x} \pm 2 s, \bar{x} \pm 3 s\), and determine the percent of measurements falling in each. If the data are approximately normal then the percentages will be approximately \(68 \%, 95 \%, 99.7 \%\) respectively.
3. Find the interquartile range \(\left(\mathrm{IQR}=\mathrm{Q}_{3}-Q_{1}\right)\) and divide it by the standard deviation \((s)\). i.e. \(\frac{Q_{3}-Q_{1}}{s}\). If \(\frac{I Q R}{S} \approx 1.3\), then the data are approximately normal.
4. Construct a normal probability plot for the data. If the points fall approximately in a straight line then the data are approximately normal. A normal probability plot is a graph with ranked data values on the horizontal axis and their corresponding quantile z-scores on the vertical axis. To find a quantile z - score :

Rank the data and beginning with the first score \(z=\operatorname{inv} \operatorname{Norm}\left(\frac{k}{2 n}\right)\) where \(k=1,3,5,7, \ldots\) and \(n\) is the number of data. See page 303 .

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