Question

Suppose there is a random sample of 1,048 observations, divided into four groups. The table below summarizes the observations that were seen in each group.

Group 1	Group 2	Group 3	Group 4
493	189	115	251

We are interested in testing the Null hypothesis Observed=Expected, under the assumption that the expected proportions are  .50, .20, .10, and .20 for the 4 groups, respectively.

What are the expected values?

Group 1	Group 2	Group 3	Group 4

What is the value of the test statistic? Round your response to at least 3 decimal places.

What is the P-value for the test? Round your response to at least 4 decimal places.

Answer 1

The null and alternative hypothesis is

Ho: P1 = 0.50 , P2 = 0.20 , P3 = 0.10 , P4 = 0.20

H1: P1 0.50 , P2 0.20 , P3 0.10 , P4 0.20

Level of significance = 0.05

Test statistic is

O: Observed frequency

E: Expected frequency.

E = n*pi

	O	p	E	(O-E)	(O-E)^2	(O-E)^2/E
	493	0.5	524	-31	961	1.833969
	189	0.2	209.6	-20.6	424.36	2.024618
	115	0.1	104.8	10.2	104.04	0.992748
	251	0.2	209.6	41.4	1713.96	8.17729
Total	1048					13.03

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

P-value = 0.0046

P-value < 0.05 we reject null hypothesis.

Conclusion: At least one proportion is not correct.