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

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

(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?

normalbinomial Student's
*t*chi-squareuniform

What are the degrees of freedom?

(c) Find or estimate the *P*-value of the sample test
statistic. (Round your answer to four 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 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

a) level of significance =0.05

H0: The distributions are the same.

H1: The distributions are different.

b)

applying chi square goodness of fit test:

observed | Expected | residual | Chi square | ||

age | Probability(p) | O_{i} |
E_{i}=total*p |
R_{i}=(O_{i}-E_{i})/√E_{i} |
R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} |

<5 | 0.072 | 45.000 | 32.76 | 2.14 | 4.57 |

5-14 | 0.136 | 74.000 | 61.88 | 1.54 | 2.37 |

15-64 | 0.671 | 286.000 | 305.31 | -1.10 | 1.22 |

>=65 | 0.121 | 50.000 | 55.06 | -0.68 | 0.46 |

total | 1 | 455 | 455 | 1.893110054 | 8.632 |

chi-square statistic =8.632

Are all the expected frequencies greater than 5? --Yes

sampling distribution will you use? -- chi-square

degrees of freedom =number of categories-1=4-1=3

c) P-value of the sample test statistic =0.0346

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%
45
5 to 14
13.6%
82
15 to 64
67.1%
288
65 and older
12.1%
40
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%
74
15 to 64
67.1%
282
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%
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...

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%
44
5 to 14
13.6%
80
15 to 64
67.1%
289
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%
80
15 to 64
67.1%
280
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...

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%
282
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%
45
5 to 14
13.6%
71
15 to 64
67.1%
298
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%
50
5 to 14
13.6%
71
15 to 64
67.1%
289
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%
46
5 to 14
13.6%
80
15 to 64
67.1%
283
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%
49
5 to 14
13.6%
80
15 to 64
67.1%
276
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...

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