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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. Observed Number Households of Households in the Community Married with children 26% 98 Married, no children 29% 125 Single parent 9% 35 One person 25% 90 Other (e.g., roommates, siblings) 11% 63 LA 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? 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 different. O Ho: The distributions are different. H1 : The distributions are the same O Ho: The distributions are the same. H,: 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 O No What sampling distribution will you use? O normal O Student's t O chi-square O uniform O binomial 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. Since the P-value > a, we reject the null hypothesis. Since the P-value S a, we reject the null hypothesis. 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. 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. Submit Answer 8. [-/5.3 Points] DETAILS BBUNDERSTAT12 10.2.007.S. MY NOTES ASK YOUR TEACHER The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site. Regional Raw Material Percent of Observed Number of Tools Stone Tools as Current excavation Site Basalt 61.3% 902 Obsidian 10.60 160 Welded T 11.40 179 Pedernal chert 13.10 194 Other 3.6% LA USE SALT Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site. a) What is the level of significance? State the null and alternate hypotheses. O Ho: The distribution e different. H : The distributions are the same. 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 the same. H, : The distributions are different. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) Are all the expected frequencies greater than 5? Yes O No What sampling distribution will you use? O binomial O chi-square O normal O uniform O Student's t What are the degrees of freedom? c) Find or estimate the P-value of the sample test statistic. O P-value > 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis Since the P-value S a, we reject the null hypothesis. 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 0.01 level of significance, the evidence is sufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site. At the 0.01 level of significance, the e is insufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site
