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%	51
5 to 14	13.6%	65
15 to 64	67.1%	296
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 the same.
H₁: The distributions are the same.H₀: The distributions are the same.
H₁: The distributions are different.    H₀: The distributions are different.
H₁: The distributions are different.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?

YesNo    

What sampling distribution will you use?

normalStudent's t    uniformbinomialchi-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 is 5%

Null and Alternate Hypothesis:

Null Hypothesis: Ho - The distributions are the same

Alternate Hypothesis: Ha - The distributions are the different

b) Chi-square statistic:

Following formula can be used to calculate the chi-square statistic:

The Expected Value can be calculated by multiplying the percentage with the total of observed values

Putting given values in the chi-square formula we get:

Chi-square = 13.229

Yes all the expected frequencies are greater than 5

Degrees of freedom:

df = k-1

where, df = degrees of freedom and k = number of values

df = 4-1= 3

Uniform binomial chi-square test will be used

C) Estimating the P-value:

By referring to the chi-square distribution table, the p-value at chi-square = 3 and df = 3 is 0.004167

Hence, P-value < 0.005

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.