Question

i need step by step help calculating the chi-square statistic for the sample, the degrees of freedom and

the P-value of the sample test statistic

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. 

Households Observed Number 

of Households in 

the Community

Married with children 26%  –   99       

Married, no children 29%  –   110       

Single parent 9%   –  36       

One person 25% –    99       

Other (e.g., roommates, siblings) 11% –    67 

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 the same.

H₁: The distributions are different.

H₀: The distributions are different.

H₁: 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

No

What sampling distribution will you use?

normal

chi-square    

uniform

Student’s t

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.) 

 

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