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.

Type of Household	Percent of U.S. Households	Observed Number of Households in the Community
Married with children	26%	94
Married, no children	29%	133
Single parent	9%	29
One person	25%	88
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.

a H₀: The Dove Creek households distribution does not fit the U.S. households distribution.
H₁: The Dove Creek households distribution fit the U.S. households distribution.

b H₀: The Dove Creek households distribution does not fit the U.S. households distribution.
H₁: The Dove Creek households distribution does not fit the U.S. households distribution.

c H₀: The Dove Creek households distribution fit the U.S. households distribution.
H₁: The Dove Creek households distribution fit the U.S. households distribution.

d H₀: The Dove Creek households distribution fit the U.S. households distribution.
H₁: The Dove Creek households distribution does not fit the U.S. households distribution.

(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?

a Yes

b No   

What sampling distribution will you use?

a binomial

b chi-square

c normal

d Student's t

e uniform

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.)

_____________

Answer 1

The statistical software output for this problem is :

(a)

level of significance = 0.05

d H₀: The Dove Creek households distribution fit the U.S. households distribution.
H₁: The Dove Creek households distribution does not fit the U.S. households distribution.

(b)

the chi-square statistic = 17.493

Yes chi square

Degrees of freedom = 4

(c)

P-value = 0.002