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% | 100 |
Married, no children | 29% | 118 |
Single parent | 9% | 30 |
One person | 25% | 93 |
Other (e.g., roommates, siblings) | 11% | 70 |
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 different.
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 the
same.
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?
YesNo
What sampling distribution will you use?
normalStudent's t uniformchi-squarebinomial
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.
observed | expexted | chi squre values |
100 | 106.2 | 0.341 |
118 | 119.19 | 0.012 |
30 | 36.99 | 1.321 |
93 | 102.75 | 0.925 |
70 | 45.21 | 13.593 |
a)level of significance is 0.05
b)H0: The distributions are the same.
H1: The distributions are different
c)chi-square statistic for the sample is 16.192
yes,Are all the expected frequencies greater than 5.
we will use normal sampling distribution.
degree of freedom is 4.
c) P-Value is .002772
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...
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% 118 Single parent 9% 28 One person 25% 97 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...
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. Observed Number of Households in the Community 90 Type of Household Married with children Married, no children Single parent One person Other (e.g., roommates, siblings) Percent of U.S. Households 26% 29% 9% 25% 11% 126 28 100 67 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 the community Dove Creek, Montana, are shown (based on Statistical Abstract of the United States) Observed Number of Percent of U.S. Households in Type of Househol Households Dove Creek 102 26% Married with children 112 29% Married, no children Single parent 9% One person 25% 96 11% Other (e.g., roommates, siblings) 68 Use a 5% level of significance to test the claim that...
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 43 5 to 14 13.6% 73 15 to 64 67.1% 297 65 and older 12.1% 42 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 43 5 to 14 13.6% 73 15 to 64 67.1% 297 65 and older 12.1% 42 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 52 5 to 14 13.6% 75 15 to 64 67.1% 282 65 and older 12.1% 46 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below. Age (years) Percent of Canadian Population Observed Number in the Village Under 5 7.2% 48 5 to 14 13.6% 79 15 to 64 67.1% 281 65 and older 12.1% 47 Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age...
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