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% | 74 |
15 to 64 | 67.1% | 296 |
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 distribution of the residents of Red Lake Village.
(a) What is the level of significance?
State the null and alternate hypotheses.
(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?
normal
Student's t
uniform
chi-square
binomial
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.
The statistic software output for this problem is:
(a)
Level of significance = 0.05
H0 : p1 = 0.072 , p2 = 0.136 , p3 = 0.671 , p4 , 0.121
H1: p1 0.072 , p2 0.136 , p3 0.671 , p4 0.121
(b)
the chi-square statistic = 10.102
Yes
chi square
Degrees of freedom = 3
(c)
0.010 < P-value < 0.025
(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...
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...
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...
Question 17 Suppose the age distribution of the Canadian population and the age distribution of a random sample of 450 residents in the Indian community of Red Lake are shown below Observed Number Percent of Canadian Age lyears) Under 5 7.4% 510 14 10.8% 151064 700% 65 and older in Red Lake Village 58 301 11 .8% 58 Use alpha-0.1 to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents...
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Suppose the age distribution of the Canadian population and the age distribution of a random sample of 528 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 6.4% 38 5 to 14 11.8% 48 15 to 64 70.3% 397 65 and older 11.5% 45 Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the...
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% 83 15 to 64 67.1% 272 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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