Question

The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below. Type of Household Percent of U.S. Households Observed Number of Households in the Community Married with children 26% 103 Married, no children 29% 105 Single parent 9% 37 One person 25% 100 Other (e.g., roommates, siblings) 11% 66 Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution. (a) What is the level of significance? State the null and alternate hypotheses. H0: The distributions are the same. H1: The distributions are different. H0: The distributions are different. H1: The distributions are different. H0: The distributions are the same. H1: The distributions are the same. H0: The distributions are different. H1: The distributions are the same. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.) Are all the expected frequencies greater than 5? Yes No What sampling distribution will you use? chi-square binomial Student's t uniform normal What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, the evidence is sufficient to conclude that the community household distribution does not fit the general U.S. household distribution. At the 5% level of significance, the evidence is insufficient to conclude that the community household distribution does not fit the general U.S. household distribution.

Answer 1

(a) What is the level of significance?

0.05

State the null and alternate hypotheses.

H0: The distributions are the same. H1: The distributions are different.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.)

11.463

Are all the expected frequencies greater than 5?

Yes

What sampling distribution will you use?

chi-square

What are the degrees of freedom?

4

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

0.022

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value ≤ α, we reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is sufficient to conclude that the community household distribution does not fit the general U.S. household distribution.

observed	expected	O - E	(O - E)² / E
103	106.860	-3.860	0.139
105	119.190	-14.190	1.689
37	36.990	0.010	0.000
100	102.750	-2.750	0.074
66	45.210	20.790	9.560
411	411.000	0.000	11.463
11.463	chi-square
4	df
.022	p-value

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