Question

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%	46
5 to 14	13.6%	70
15 to 64	67.1%	298
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.

H₀: The distributions are different.
H₁: The distributions are the same.H₀: The distributions are different.
H₁: The distributions are different.    H₀: The distributions are the same.
H₁: The distributions are the same.H₀: The distributions are the same.
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?

binomialuniform    Student's tnormalchi-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 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.    

Answer 1

(a) The Level of significance = 0.01

The Hypothesis: Option 4:

H0: The distributions are the same.

H1: The distributions are different.

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(b) The Test Statistic: Each expected value = (Expected%/100) * Total. Here total = 455

	Observed	Expected %	Expected	(O-E)2	(O-E)2/E
Under 5	46	7.2	32.76	175.2976	5.35096
5-14'	70	13.6	61.88	65.9344	1.06552
15-64	298	67.1	305.305	53.363025	0.17479
65+	41	12.1	55.055	197.54303	3.58810
Total	455.00	100.00	455.00	492.14	10.179

= 10.179

All expected frequencies are > 5: YES

Which distribution is Used: For a Goodness of fit, we use the chi square distribution.

The degrees of freedom = n - 1 = 4 - 1 = 3

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(c) The p value for the given test statistic (10.179) = 0.0171

Therefore the range of the p value   0.01 < p-value < 0.025

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(d) Option 3: Since p value is , we reject the null hypothesis.

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(e) Option 2: 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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