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% | 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.
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.
H0: The distributions are different.
H1: 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.
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
H0: The distributions are the same.
H1: 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.
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