a) State the null and alternate hypotheses. H0: The distributions are different. H1: The distributions are the same. 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 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.) (c) What sampling distribution will you use? uniform binomial normal chi-square Student's t (d) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) (e) 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. (f) 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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%	122
Single parent	9%	30
One person	25%	92
Other (e.g., roommates, siblings)	11%	64

(a) State the null and alternate hypotheses.

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

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 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.)

(c) What sampling distribution will you use?

uniform

binomial

normal

chi-square

Student's t

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

(e) 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.

(f) 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.

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