The type of household for the U.S. population and for a randomsample of 411 households from a community in Montana are shownbelow.

Type of Household	Percent of U.S. Households	Observed Number of Households in the Community
Married with children	26%	105
Married, no children	29%	111
Single parent	9%	33
One person	25%	93
Other (e.g., roommates, siblings)	11%	69

Use a 5% level of significance to test the claim that thedistribution of U.S. households fits the Dove Creekdistribution.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are the same.
H₁: The distributions aredifferent.H₀: The distributions are thesame.
H₁: The distributions are thesame.    H₀: Thedistributions are different.
H₁: The distributions are thesame.H₀: The distributions are different.
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 thetest statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

binomialStudent'st    normalchi-squareuniform

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample teststatistic. (Round your answer to three decimal places.)


(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis that the population fits thespecified distribution of categories?

Since the P-value > ?, we fail to rejectthe null hypothesis.Since the P-value > ?, wereject the null hypothesis.    Since theP-value ? ?, we reject the null hypothesis.Sincethe P-value ? ?, we fail to reject the nullhypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, the evidence is sufficient toconclude that the community household distribution does not fit thegeneral U.S. household distribution.At the 5% level ofsignificance, the evidence is insufficient to conclude that thecommunity household distribution does not fit the general U.S.household distribution.