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%	292
65 and older	12.1%	47

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.

1 What is the level of significance?


2 State the null and alternate hypotheses.

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

3) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)


4 Are all the expected frequencies greater than 5?

Yes No    

5 What sampling distribution will you use?

uniform

Student's t   

chi-square

binomial

normal

6 What are the degrees of freedom?


7 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 < 0.010

P-value < 0.005

8 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.

9 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

1 What is the level of significance?
0.05

2 State the null and alternate hypotheses.

OPTION a)

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

 

3) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

TS = 12.071

4 Are all the expected frequencies greater than 5?

Yes

5 What sampling distribution will you use?

chi-square

6 What are the degrees of freedom?
df = 3

7 Estimate the P-value of the sample test statistic.

p-value =

0.007144

.005 < P-value < 0.010

8 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 reject the null hypothesis.

9 Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.