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% | 50 |

5 to 14 | 13.6% | 67 |

15 to 64 | 67.1% | 295 |

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?

Yes No

What sampling distribution will you use?

chi-square

Student's *t*

normal

binomial

uniform

What are the degrees of freedom?

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

*P*-value > 0.100

0.050 < *P*-value < 0.100

0.025 < *P*-value < 0.050

0.010 < *P*-value < 0.025

0.005 < *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 statistic software output for this problem is :

Chi-Square goodness-of-fit results:

Observed: O

Expected: E

N | DF | Chi-Square | P-value |
---|---|---|---|

455 | 3 | 12.483632 | 0.0059 |

Observed | Expected |
---|---|

50 | 32.76 |

67 | 61.88 |

295 | 305.305 |

43 | 55.055 |

(a)

The level of significance = 0.05

H_{0}: The distributions are the same.

H_{1}: The distributions are different.

(b)

chi-square statistic = 12.484

Yes

Chi square

degrees of freedom = 3

(c)

0.005 < *P*-value < 0.010

(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 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%
52
5 to 14
13.6%
77
15 to 64
67.1%
277
65 and older
12.1%
49
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%
47
5 to 14
13.6%
68
15 to 64
67.1%
295
65 and older
12.1%
45
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% 70 15 to 64 67.1% 283 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%
50
5 to 14
13.6%
78
15 to 64
67.1%
286
65 and older
12.1%
41
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%
80
15 to 64
67.1%
278
65 and older
12.1%
45
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% 50
5 to 14 13.6% 75 15 to 64 67.1% 280 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%
47
5 to 14
13.6%
72
15 to 64
67.1%
290
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% 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%
50
5 to 14
13.6%
71
15 to 64
67.1%
286
65 and older
12.1%
48
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%
49
5 to 14
13.6%
67
15 to 64
67.1%
292
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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