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 Numberof Households in the Community |

Married with children | 26% | 103 |

Married, no children | 29% | 118 |

Single parent | 9% | 34 |

One person | 25% | 90 |

Other (e.g., roommates, siblings) | 11% | 66 |

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.

*H*_{0}: The distributions are different.

*H*_{1}: The distributions are
different.*H*_{0}: The distributions are the
same.

*H*_{1}: The distributions are
different. *H*_{0}: The
distributions are different.

*H*_{1}: The distributions are the
same.*H*_{0}: The distributions are the same.

*H*_{1}: 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

uniform

chi-square

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.)

___________________

(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 > *α*, we fail to reject
the null hypothesis.

Since the *P*-value > *α*, we reject the null
hypothesis.

Since the *P*-value ≤ *α*, we reject the null
hypothesis.

Since the *P*-value ≤ *α*, 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.

Answer #1

a)

Significance level = 0.05

H0: The distributions are the same.

H1: The distributions are different.

b)

Type of Household | Expected Percentage | Observed Number | Expected Number | (Oi - Ei)^2/Ei |

Married with children | 26% | 103 | 106.86 | 0.139 |

Married, no children | 29% | 118 | 119.19 | 0.012 |

Single parent | 9% | 34 | 36.99 | 0.242 |

One person | 25% | 90 | 102.75 | 1.582 |

Other (e.g., roommates, siblings) | 11% | 66 | 45.21 | 9.560 |

411 | 11.535 |

Test statistic, chi-square = sum((Oi - Ei)^2/Ei)

All expected frequencies are greater than 5 - Yes

sampling distribution - chi-square

degrees of freedom = 5 - 1 = 4

c)

p-value = 0.021

d)

Since the P-value ≤ α, 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.

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%
96
Married, no children
29%
113
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
73
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
104
Married, no children
29%
112
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
66
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
93
Married, no children
29%
127
Single parent
9%
35
One person
25%
88
Other (e.g., roommates, siblings)
11%
68
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
98
Married, no children
29%
118
Single parent
9%
38
One person
25%
91
Other (e.g., roommates, siblings)
11%
66
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
97
Married, no children
29%
119
Single parent
9%
35
One person
25%
95
Other (e.g., roommates, siblings)
11%
65
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
92
Married, no children
29%
120
Single parent
9%
29
One person
25%
101
Other (e.g., roommates,
siblings)
11%
69
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
105
Married, no children
29%
110
Single parent
9%
36
One person
25%
91
Other (e.g., roommates, siblings)
11%
69
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
101
Married, no children
29%
110
Single parent
9%
32
One person
25%
97
Other (e.g., roommates, siblings)
11%
71
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
91
Married, no children
29%
130
Single parent
9%
29
One person
25%
97
Other (e.g., roommates, siblings)
11%
64
Use a 5% level of significance to test the claim that the
distribution of U.S. households fits the...

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%
105
Married, no children
29%
120
Single parent
9%
28
One person
25%
91
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...

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