Q. 6.127 - Elementary Statistics

Question

A sample of final exam scores in a large introductory statistics course is as follows.

Part (a): Use Table III in Appendix A to construct a normal probability plot of the given data.

Part (b): Use part (a) to identify any outliers.

Part (c): Use part (a) to access the normality of the variable under consideration.

Step-by-Step Solution

Answer

Part (a): The required normal probability plot is given below,

Part (b): On identifying the outliers, we get $34$ and $39$.

Part (c): Final-exam scores in this introductory statistics class do not appear to be normally distributed.

Part (a) Step 1. Given information.

Consider the given question,

Part (a) Step 2. Construct a normal probability plot.

The variable is final exam score. To construct a normal probability plot, we first arrange the data in increasing order and obtain the normal scores from normal scores table.

The ordered data are shown in the first column of the below table; the normal scores form $n=20$ column of normal scores table, are shown in the second column of the below table.

Part (a) Step 3. Plot the points.

Plot the points using horizontal axis for the final exam scores and the vertical axis for the normal scores,

Part (b) Step 1. Identify any outliers.

Consider the normal probability plot from part (a),

We can observe the final exam scores, $34,39$ are outliers.

These two observations fall outside the overall pattern of the data.

Part (c) Step 1. Access the normality of the variable under consideration.

Consider the normal probability plot from part (a),

The above normal probability plot is not roughly linear. So, we can assume that the final exam score is not approximately normally disturbed.