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%	78
15 to 64	67.1%	282
65 and older	12.1%	49

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

Yes

No    

What sampling distribution will you use?

chi-square

uniform

normal

Student's t

binomial

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 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

Hypotheses are

H0: The distributions are the same.

H1: The distributions are different.  

(b)

Following table shows the calculations:

Age (years)	Percent of Canadian Population	Observed Number in the Village, O	E=p*455	(O-E)^2/E
Under 5	0.072	46	32.76	5.350964591
5 to 14	0.136	78	61.88	4.199327731
15 to 64	0.671	282	305.305	1.778952277
65 and older	0.121	49	55.055	0.66593452
Total	1	455	455	11.99517912

Following is the test statistics:

Are all the expected frequencies greater than 5?

Yes

What sampling distribution will you use?

chi-square

What are the degrees of freedom?

df= 4-1=3

(c)

From chi square table:

From table, the p-value is between 0.01 and 0.025.

Correct option:

0.005 < P-value < 0.010

(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.