Question

The amounts of financial aid awarded for a population of students are shown below. Using an appropriate graphical technique, state whether you believe that the assumption of normality of this population of aid awards exists. Justify your answer.

$8,500 $11,000 $12,400 $9,000 $14,000 $4,500 $12,000 $16,000 $7.500 $11,500 $8.000 $19,000 $10,500 $5,000 $16,500 $9,500 $20,000 $17,500 $8.500 $12,500 $7,000 $19,000 $19,500 $6,000 $13,000

Answer 1

We will use normal probability plot to check that is from normal distribution or not.

Normal probability plot-

Observation table -

X	Rank	Cumulative prob	Z
8500	7.5	0.28	-0.58
11000	12	0.46	-0.1
12400	15	0.58	0.2
9000	9	0.34	-0.41
14000	18	0.7	0.52
4500	1	0.02	-2.05
12000	14	0.54	0.1
16000	19	0.74	0.64
7500	5	0.18	-0.92
11500	13	0.5	0
8000	6	0.22	-0.77
19000	22.5	0.88	1.17
10500	11	0.42	-0.2
5000	2	0.06	-1.55
16500	20	0.78	0.77
9500	10	0.38	-0.31
20000	25	0.98	2.05
17500	21	0.82	0.92
8500	7.5	0.28	-0.58
12500	16	0.62	0.31
7000	4	0.14	-1.08
19000	22.5	0.88	1.17
19500	24	0.94	1.55
6000	3	0.1	-1.28
13000	17	0.66	0.41

Cumulative probability = (i - 0.5)/n

where, i = rank of X & n = total sample size

Value of Z calculated from table provided below.

In normal probability plot, points are approximately close to staight line. A straight line in a normal probability plot is a strong indication of data normally distributed.

Hence, the assumption of normality of this population of aid awards exists.