In Figure 4.19, we visually inspected the relative frequency histogram for sample means ba...

In Figure 4.19, we visually inspected the relative frequency histogram for sample means based on two measurements and noted its bell shape. Another way to determine whether a set of measurements is bell shaped (normal) is to construct a normal probability plot of the sample data. If the plotted points are nearly a straight line, we say the measurements were selected from a normal population. We can generate a normal probability plot using the following Minitab code. If the plotted points fall within the curved dotted lines, we consider the data to be a random sample from a normal distribution.

Minitab code:

1. Enter the 45 measurements into C1 of the data spreadsheet.

2. Click on Graph, then Probability Plot.

3. Type c1 in the box labeled Variables:.

4. Click on OK.

The 45 data valu.es clearly fall within the two curved lines and fairly close to the straight line. Thus, we conclude there is a strong indication that the data values follow a normal distribution.

a. Suppose our population was the 10 measurements (2, 3, 6, 8, 9, 12, 25, 29, 39, 50). Generate the 45 sample means based on n = 2 observations per sample and determine whether the sampling distribution of the sample mean is approximately normally distributed by constructing a histogram and normal probability plot of the 45 sample means.

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b. Why do you think the plots for the means from the population (2, 3, 6, 8, 9, 12, 25, 29, 39, 50) differ greatly from the plots obtained for the means from the population (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)?

Figure 4.19: Sampling distribution for