The type of household for the U.S. population and for a random sample of 411 hou

Question

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.

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.

H0: The distributions are the same.
H1: The distributions are the same.

H0: The distributions are different.
H1: The distributions are different.  

  H0: The distributions are different.
H1: The distributions are the same.

H0: 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.)


Are all the expected frequencies greater than 5?

Yes or No    

What sampling distribution will you use?

uniform . Student's t    normal . chi-square . 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?

Since the P-value > ?, we fail to reject the null hypothesis. Since the P-value > ?, we reject the null hypothesis.   

Since the P-value ? ?, we reject the null hypothesis. Since the P-value ? ?, we fail to reject the null hypothesis.

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

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.    

Type of Household Percent of U.S.
Households Observed Number
of Households in
the Community Married with children 26%         91             Married, no children 29%         118             Single parent 9%         37             One person 25%         95             Other (e.g., roommates, siblings) 11%         70            

Explanation / Answer

a)e level of significance =0.05

H0: The distributions are the same.
H1: The distributions are different.

b)

applying chi square test:

  test statistic =16.543 (please try 16.544 if this comes wrong)

Are all the expected frequencies greater than 5? --Yes

What sampling distribution will you use?--chi square

degrees of freedom? -- categories-1=5-1=4

c)

P-value of the sample test statistic. =0.002

d)

Since the P-value ? ?, we reject the null hypothesis.

e)

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.

category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei married with children 0.260 91.000 106.86 2.354 married ,no children 0.290 118.000 119.19 0.012 single parent 0.090 37.000 36.99 0.000 one person 0.250 95.000 102.75 0.585 other 0.110 70.000 45.21 13.593 total 411 411 16.543

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