Question

(S 12.1) 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	Group 2	Group 3	Group 4
24	38	50	34

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

H0: p1 = p2 = p3 = p4 = 0.25

HA: At least 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
	24	36.5	-12.5	156.25	4.280822
	38	36.5	1.5	2.25	0.061644
	50	36.5	13.5	182.25	4.993151
	34	36.5	-2.5	6.25	0.171233
Total	146				9.51

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

P-value = P( ) = 0.0233

P-value < 0.05 we reject null hypothesis.

Conclusion:

At least one proportion is incorrect.