Question

Use α = 0.01 and conduct a goodness of fit test using 5 classes to see whether the following sample appears to have been selected from a normal probability distribution.

(Note: x = 70 and s = 18.)

55	86	94	58	55	95	55	52	69	95	90	65	87	50	56
55	57	98	58	79	92	62	59	88	40

Find the value of the test statistic.

Find the p-value. (Round your answer to four decimal places.)

p-value =

Answer 1

Goodness of Fit test(Chi square):

Ho: To test the data is distributed normally and sampled from normal distribution

Ha: To test the data is not distributed normally and sample is not normal

Significant level: 0.01

The degree of freedom: n-1

n=25

DF=25-1=24

Significant value: $\chi ^2_{df,\alpha }= \chi ^2_{24,0.01}=42.98$

Distribution Plot Chi-Square, df 24 0.06 0.05 0.04- 0.03 0.02 0.01 0.01 0.00 42.98

The test statistic:

$\chi ^2= \frac{\sum (O_i-E_i)^2}{E_i}$

O- Observation, E- Expected value(Mean)

X	Mean	(X-mean)^2/Mean
55	70	3.214285714
86	70	3.657142857
94	70	8.228571429
58	70	2.057142857
55	70	3.214285714
95	70	8.928571429
55	70	3.214285714
52	70	4.628571429
69	70	0.014285714
95	70	8.928571429
90	70	5.714285714
65	70	0.357142857
87	70	4.128571429
50	70	5.714285714
56	70	2.8
55	70	3.214285714
57	70	2.414285714
98	70	11.2
58	70	2.057142857
79	70	1.157142857
92	70	6.914285714
62	70	0.914285714
59	70	1.728571429
88	70	4.628571429
40	70	12.85714286
	Sum	111.8897

$\chi ^2= \frac{\sum (O_i-E_i)^2}{E_i}=111.8857$

P-value: 0.0000

The test statistic is significant and rejects H0, that the sample is not normally distributed.