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. \begin{tabular}{|c|c|c|} \hline Type of Household & \begin{tabular}{c} Percent of U.S. \\ Households \end{tabular} & \begin{tabular}{c} Observed Number \\ of Households in \\ the Community \end{tabular} \\ \hline Married with children & \( 26 \% \) & 104 \\ \hline Married, no children & \( 29 \% \) & 117 \\ \hline Single parent & \( 9 \% \) & 29 \\ \hline One person & \( 25 \% \) & 94 \\ \hline Other (e.g., roommates, siblings) & \( 11 \% \) & 67 \\ \hline \end{tabular} \( \Omega \) USE SALT 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? \( \square \) State the null and alternate hypotheses. \( H_{0} \) : The distributions are different. \( H_{1} \) : The distributions are the same.
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The level of significance for this hypothesis test is given as 5%, which means that there is a 5% risk of concluding that the distributions are different when they are actually the same. This is denoted as \( \alpha = 0.05 \). Show more…
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The type of household for the U.S. population and for a random sample of 411 households from the Dove Creek 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% 93 Married, no children 29% 121 Single parent 9% 36 One person 25% 89 Other (e.g., roommates, siblings) 11% 72 Use a 5% level of significance to test the claim that the Dove Creek distribution fits the distribution of U.S. households. What sampling distribution will you use for this test? Are all the expected frequencies greater than 5? (Round the expected frequencies to two decimal places.) What are the degrees of freedom for this test? What is the critical value for this test separating the fail to reject and reject regions? Find the value of the sample test statistic for this test: (Round the test statistic to three decimal places.) Will you fail to reject or reject the null hypothesis? State your conclusion in context of the problem: At 5% level of significance, (fail to reject or reject) the null hypothesis. There is (insufficient or sufficient) evidence to find that the Dove Creek households distribution does not fit the U.S. households distribution.
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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. Type of Household Percent of U.S. Households Observed Number of Households in the Community Married with children 26% 96 Married, no children 29% 123 Single parent 9% 29 One person 25% 98 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. (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.) 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.)
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