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. Observed Number of Households in the Community Percent of U.S. Type of Household Households Married with children 26% 100 Married, no children 29% 107 Single parent 9% 37 One person 25% 102 Other (e.g., roommates, siblings) 11% 65 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. O Ho: The distributions are different. H,: The distributions are different. O Hn: The distributions are the same. H,: The distributions are the same. O Hn: The distributions are different. H, : The distributions are the same. O Ho: The distributions are the same. H,: 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.) Are all the expected frequencies greater than 5? O Yes O No What sampling distribution will you use? O Student's t O normal O chi-square O binomial O uniform What are the degrees of freedom?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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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.
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.
Observed Number
Percent of U.S.
Type of Household
of Households in
Households
the Community
Married with children
26%
100
Married, no children
29%
107
Single parent
9%
37
One person
25%
102
Other (e.g., roommates, siblings)
11%
65
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.
O Ho: The distributions are different. H, : The distributions are different.
O Ho: The distributions are the same. H,: The distributions are the same.
O Ho: The distributions are different. H, : The distributions are the same.
O Ho: The distributions are the same. H,: 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.)
Are all the expected frequencies greater than 5?
O Yes
O No
What sampling distribution will you use?
O Student'st
O normal
O chi-square
O binomial
O uniform
What are the degrees of freedom?
Transcribed Image Text: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. Observed Number Percent of U.S. Type of Household of Households in Households the Community Married with children 26% 100 Married, no children 29% 107 Single parent 9% 37 One person 25% 102 Other (e.g., roommates, siblings) 11% 65 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. O Ho: The distributions are different. H, : The distributions are different. O Ho: The distributions are the same. H,: The distributions are the same. O Ho: The distributions are different. H, : The distributions are the same. O Ho: The distributions are the same. H,: 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.) Are all the expected frequencies greater than 5? O Yes O No What sampling distribution will you use? O Student'st O normal O chi-square O binomial O uniform 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?
O Since the P-value > a, we fail to reject the null hypothesis.
O Since the P-value > a, we reject the null hypothesis.
O Ssince the Pp-value sa, we reject the null hypothesis.
O since the P-value s a, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O 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.
O 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.
Transcribed Image Text:(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? O Since the P-value > a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Ssince the Pp-value sa, we reject the null hypothesis. O since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O 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. O 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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