The age distribution of the Canadian population and the age distribution of a random sample of...
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The age distribution of the Canadian population and the agedistribution of a random sample of 455 residents in the Indiancommunity of a village are shown below.
Age(years) Percent of CanadianPopulation Observed Number
in the Village Under 5 7.2% 50 5 to 14 13.6% 81 15 to 64 67.1% 284 65 and older 12.1% 40
Use a 5% level of significance to test the claim that the agedistribution of the general Canadian population fits the agedistribution 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 different.
H1: The distributions are thesame. H0: Thedistributions are the same.
H1: The distributions are different.H0: The distributions are the same.
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?
uniform chi-square binomial normalStudent's t
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 orfail to reject the null hypothesis that the population fits thespecified distribution of categories?
Since the P-value > ?, we fail to rejectthe null hypothesis. Since the P-value > ?, wereject the null hypothesis. Since theP-value ? ?, we reject the null hypothesis. Sincethe P-value ? ?, we fail to reject the nullhypothesis.
(e) Interpret your conclusion in the context of theapplication.
At the 5% level of significance, the evidence is insufficient toconclude that the village population does not fit the generalCanadian population. At the 5% level of significance, the evidenceis sufficient to conclude that the village population does not fitthe general Canadian population.
The age distribution of the Canadian population and the agedistribution of a random sample of 455 residents in the Indiancommunity of a village are shown below.
| Age(years) | Percent of CanadianPopulation | Observed Number in the Village |
| Under 5 | 7.2% | 50 |
| 5 to 14 | 13.6% | 81 |
| 15 to 64 | 67.1% | 284 |
| 65 and older | 12.1% | 40 |
Use a 5% level of significance to test the claim that the agedistribution of the general Canadian population fits the agedistribution 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 different.
H1: The distributions are thesame. H0: Thedistributions are the same.
H1: The distributions are different.H0: The distributions are the same.
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?
uniform chi-square binomial normalStudent's t
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 orfail to reject the null hypothesis that the population fits thespecified distribution of categories?
Since the P-value > ?, we fail to rejectthe null hypothesis. Since the P-value > ?, wereject the null hypothesis. Since theP-value ? ?, we reject the null hypothesis. Sincethe P-value ? ?, we fail to reject the nullhypothesis.
(e) Interpret your conclusion in the context of theapplication.
At the 5% level of significance, the evidence is insufficient toconclude that the village population does not fit the generalCanadian population. At the 5% level of significance, the evidenceis sufficient to conclude that the village population does not fitthe general Canadian population.
Answer & Explanation Solved by verified expert
a) level of significance=0.05
H0: The distributions are the same.
H1: The distributions are different.
b)
applying chi square test:
| relative | observed | Expected | residual | Chi square | |
| category | frequency(p) | Oi | Ei=total*p | R2i=(Oi-Ei)/?Ei | R2i=(Oi-Ei)2/Ei |
| <5 | 0.072 | 50 | 32.76 | 3.01 | 9.073 |
| 5-14 | 0.136 | 81 | 61.88 | 2.43 | 5.908 |
| 15-64 | 0.671 | 284 | 305.31 | -1.22 | 1.487 |
| 65 and older | 0.121 | 40 | 55.06 | -2.03 | 4.117 |
| total | 1.000 | 455 | 455 | 20.584 |
value of the chi-square statistic =X2=20.584
| Are all the expected frequencies greater than 5? :Yes |
| What sampling distribution will you use? chi-square |
| degrees of freedom =categories-1=3 |
c) P-value < 0.005
d)
Since the P-value ? ?, 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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