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 Canadian Population	Observed Number in the Village
Under 5	7.2%                 Â	52           Â
5 to 14	13.6%                 Â	82           Â
15 to 64	67.1%                 Â	276           Â
65 and older	12.1%                 Â	45           Â

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 thesame.H₀: The distributions are different.
H₁: The distributions aredifferent.    H₀: Thedistributions are the same.
H₁: The distributions aredifferent.H₀: The distributions are thesame.
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 or No    

What sampling distribution will you use?

uniformbinomial    Student'stnormalchi-square

What are the degrees of freedom?


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

P-value > 0.1000.050 < P-value <0.100    0.025 < P-value <0.0500.010 < P-value < 0.0250.005 <P-value < 0.010P-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 > α, we fail to rejectthe null hypothesis.Since the P-value > α, wereject the null hypothesis.    Since theP-value ≤ α, we reject the null hypothesis.Sincethe P-value ≤ α, 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.