6. 10118 points | Previous Answers My Notes The type of household for the U.S. p

Question

6. 10118 points | Previous Answers My Notes 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 Type of Household Married with children Married, no children Single parent One person Percent of U.S. Households 26% 29% 996 25% the Communi 104 28 103 65 e.q., roommates, sibli 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 H: The distributions are the same. H: The distributions are different. Ho: The distributions are the same. H: The distributions are the same. Ho: The distributions are different. H, : The distributions are the same. Ho: The distributions are different. 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.)

Explanation / Answer

a)level of significance =0.05

b)applying chi square goodness of fit test:

chi square test statistic =11.488

degree of freedom =categories-1=5-1 =4

c)

estimate p =0.022

observed Expected Chi square category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei married; with children 0.260 104.000 106.86 0.08 married; no children 0.290 111.000 119.19 0.56 single parent 0.090 28.000 36.99 2.18 one person 0.250 103.000 102.75 0.00 other 0.110 65.000 45.21 8.66 total 1 411 411 11.4876

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