7. [-15.3 Points] DETAILS BBUNDERSTAT12 10.2.006.MI.S. 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 Me of Household Pgglgf' of Households In the Community Married with children 26% 100 Married, no children 29% 111 Single parent 9% 31 One person 25% 100 Other (e.g., roommates, siblings) 11% 69 Ia use SALT MY NOTES ASK YOUR TEACHER Use a 5% level of signicance to test the claim that the distribution of U.S. households fits the Dove Creek distribution. (a) What is the level of signicance? E State the null and alternate hypotheses. : The distributions are the same. H1: The distributions are the same. D: The distributions are different. H1: The distributions are the same. D: The distributions are different. H1: The distributions are different. D: 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.) Q Are all the expected frequencies greater than 5? 0 Yes 0 No What sampling distribution will you use? 0 normal 0 Student's t O binomial O chi-square O uniform what are the degrees of freedom? E (c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three decimal places.) E (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 Since the P-value s a, 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