Constructing Normal Quantité Plots. In Exercises, use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution.

Brain Volumes A sample of human brain volumes (cm3) is obtained from those listed in Data Set 6: 1272, 1051, 1079, 1034, 1070, 1173, 1079, 1067.

Problem 19BSC

Answer:

Step1 of 3:

We have A sample of human brain volumes (cm3) is obtained from those listed in Data Set 6: 1272, 1051, 1079, 1034, 1070, 1173, 1079, 1067.

Step2 of 3:

We need to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution.

Step3 of 3:

The given data in Ascending order

1034 |
1051 |
1067 |
1070 |
1079 |
1079 |
1173 |
1272 |

Manual Construction of a Normal Quantile Plot:

Step 1. First sort the data by arranging the values in order from lowest to highest.

Step 2. With a sample of size n, each value represents a proportion of 1/n of the sample. Using the known sample size n, identify the areas of 1/2n, 3/2n, 5/2n, 7/2n, and so on. These are the cumulative areas to the left of the corresponding sample values.

Step 3. Use the standard normal distribution (Table A2 or software or a calculator) to find the z scores corresponding to the cumulative left areas found in Step 2. (These are the z scores that are expected from a normally distributed sample.)