Determine a the x2 Determine a the x2 test statistic b the X

Determine (a) the x2...

Determine (a) the x^2 test statistic, (b) the X degrees of freedom, (c) the critical value using a = 0.05, and (d) test the hypothesis at the a = 0.05 level of significance. H0: The random variable X is binomial with n = 4, p = 0.8 H1: The random variable X is not binomial with n = 4, p = 0.8

Solution

a).

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

1

1.6

-0.600

0.225

37

25.3

11.700

5.411

121

152.1

-31.100

6.359

440

405.5

34.500

2.935

391

405.5

-14.500

0.518

Total

990

990.0

0.000

15.448

Chi square test statistic = 15.448

b).

Degrees of freedom = 5-1=4

c).

critical value at 0.05 level =9.488

d).

calculated value 15.448 > 9.488 table value

The null hypothesis is rejected.

we conclude that the random variable X is not binomial with n=4, p=0.8

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	1	1.6	-0.600	0.225
	37	25.3	11.700	5.411
	121	152.1	-31.100	6.359
	440	405.5	34.500	2.935
	391	405.5	-14.500	0.518
Total	990	990.0	0.000	15.448