Question

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%                   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.

H0: The distributions are the same.
H1: The distributions are different.H0: The distributions are different.
H1: The distributions are the same.    H0: The distributions are the same.
H1: The distributions are the same.H0: The distributions are different.
H1: 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 tchi-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.  

Homework Answers

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) Oi Ei=total*p Ri=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei
<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.

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