Question

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 Numberin the Village |

Under 5 | 7.2% | 51 |

5 to 14 | 13.6% | 69 |

15 to 64 | 67.1% | 292 |

65 and older | 12.1% | 43 |

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(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 the same.

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

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

(b) Find the value of the chi-square statistic for the sample.
(Round your answer to three decimal places.)

Are all the expected frequencies greater than 5?

YesNo

What sampling distribution will you use?

Student's
*t*chi-square normalbinomialuniform

What are the degrees of freedom?

(c) Estimate the *P*-value of the sample test statistic.

*P*-value > 0.1000.050 < *P*-value <
0.100 0.025 < *P*-value <
0.0500.010 < *P*-value < 0.0250.005 <
*P*-value < 0.010*P*-value < 0.005

(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 insufficient to conclude that the village population does not fit the general Canadian population.At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population

Answer #1

The statistical software output for this problem is :

level of significance = 0.05

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

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

chi-square statistic = 14.194

Yes

chi-square

degrees of freedom = 3

*P*-value < 0.005

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

At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population

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%
45
5 to 14
13.6%
74
15 to 64
67.1%
286
65 and older
12.1%
50
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% 66 15 to 64 67.1% 299 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%
45
5 to 14
13.6%
83
15 to 64
67.1%
280
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...

Suppose the age distribution of the Canadian population and the
age distribution of a random sample of 444 residents in the Indian
community of Red Lake are shown below.
Observed Number
Age (years)
Percent of Canadian Population
in Red Lake Village
Under 5
7.3%
42
5 to 14
12.5%
47
15 to 64
68.3%
314
65 and older
11.9%
41
Use to test the claim that the age distribution of
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The type of household for the U.S. population and for a random
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Type of Household
Percent of U.S.
Households
Observed Number
of 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
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Suppose the age distribution of the Canadian population and the
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The types of browse favored by deer are shown in the following
table. Using binoculars, volunteers observed the feeding habits of
a random sample of 320 deer.
Type of Browse
Plant
Composition
in Study Area
Observed Number of
Deer
Feeding on This Plant
Sage brush
32%
110
Rabbit brush
38.7%
118
Salt brush
12%
44
Service berry
9.3%
23
Other
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25
Use a 5% level of significance to test the claim that the
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The accuracy of a census report on a city in southern California
was questioned by some government officials. A random sample of
1215 people living in the city was used to check the report, and
the results are shown below.
Ethnic
Origin
Census
Percent
Sample
Result
Black
10%
136
Asian
3%
40
Anglo
38%
465
Latino/Latina
41%
510
Native American
6%
51
All others
2%
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Using a 1% level of significance, test the claim that the census
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The Fish and Game Department stocked a lake with fish in the
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95 205 73 In the 5-year interval, did the distribution of fish
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The types of raw materials used to construct stone tools found
at an archaeological site are shown below. A random sample of 1486
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