Chapter 13: Q2CRE (page 597)

Test for Normality Use the departure delay times for Flight 19 and test for normality using a normal quantile plot.

Short Answer

Expert verified

The following normal quantile plot is constructed:

As the majority of points do not lie along a straight line, the departure delay times of Flight 19 do not come from a normally distributed population.

Step by step solution

Given information

The departure delay times (in minutes) for Flight 19 are given.

Normal quantile plot

Follow the given steps to construct a normal quantile plot:

Arrange the given values in ascending order as shown:

-5

-4

-1

Compute the cumulative areas to the left for each sample as follows:

Sample value	Areas to the left
-5	\(\begin{array}{c}\frac{1}{{2n}} = \frac{1}{{2\left( 8 \right)}}\\ = 0.0625\end{array}\)
-4	\(\begin{array}{c}\frac{3}{{2n}} = \frac{3}{{2\left( 8 \right)}}\\ = 0.1875\end{array}\)
-4	\(\begin{array}{c}\frac{5}{{2n}} = \frac{5}{{2\left( 8 \right)}}\\ = 0.3125\end{array}\)
-1	\(\begin{array}{c}\frac{7}{{2n}} = \frac{7}{{2\left( 8 \right)}}\\ = 0.4375\end{array}\)
0	\(\begin{array}{c}\frac{9}{{2n}} = \frac{9}{{2\left( 8 \right)}}\\ = 0.5625\end{array}\)
1	\(\begin{array}{c}\frac{{11}}{{2n}} = \frac{{11}}{{2\left( 8 \right)}}\\ = 0.6875\end{array}\)
19	\(\begin{array}{c}\frac{{13}}{{2n}} = \frac{{13}}{{2\left( 8 \right)}}\\ = 0.8125\end{array}\)
73	\(\begin{array}{c}\frac{{15}}{{2n}} = \frac{{15}}{{2\left( 8 \right)}}\\ = 0.9375\end{array}\)

The corresponding z-scores of the areas computed above are tabulated below:

Areas	z-scores
0.0625	-1.534
0.1875	-0.887
0.3125	-0.489
0.4375	-0.157
0.5625	0.157
0.6875	0.489
0.8125	0.887
0.9375	1.534

Now, plot the original data values on the x-axis and the corresponding z-scores on the y-axis.

Sample values (x)	z-scores (y)
-5	-1.534
-4	-0.887
-4	-0.489
-1	-0.157
0	0.157
1	0.489
19	0.887
73	1.534

Mark the values -20, 0, 20, 40, ……., 80 on the horizontal scale. Label the axis as “Sample Values”.
Mark the values -2.000, -1.500, -1.000, …….., 2.000 on the vertical axis. Label the axis as “z-score”.
Place a dot for the values of the z-scores corresponding to the sample values on the x-axis.
Draw a straight trend line.

The following normal quantile plot is obtained: