Question

Suppose there is a random sample of n observations, divided into four groups. The table below summarizes the count of observations that were seen in each group.

Group 1 -36

Group 2 -30

Group 3 -68

Group 4 -45

We are interested in testing the null hypothesis H0:p1=p2=p3=p4=0.25, against the alternative hypothesis HA:Atleastoneproportionisincorrect.

What is the expected count for each of the groups? Expected: _______

What is the value of the test statistic? _______Round your response to at least 2 decimal places.

What are the appropriate degrees of freedom? _______

What is the P-value? _______ Round to at least 4 decimal places

Answer 1

The null and alternative hypothesis is

H0: p1 = p2 = p3 = p4 = 0.25

HA:Atleast one proportion is incorrect.

Level of significance = 0 .05

Test statistic is

O: Observed frequency
E: Expected frequency.

E = n*pi

	O	E	(O-E)	(O-E)^2	(O-E)^2/E
	36	44.75	-8.75	76.5625	1.710894
	30	44.75	-14.75	217.5625	4.861732
	68	44.75	23.25	540.5625	12.07961
	45	44.75	0.25	0.0625	0.001397
Total	179				18.65

Degrees of freedom = Number of E's - 1 = 4 - 1 = 3

P-value = P( ) = 0.0003

P-value < 0.05 we reject null hypothesis.

Conclusion:

Atleast one proportion is incorrect.