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%	48
5 to 14	13.6%	79
15 to 64	67.1%	281
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.

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

Yes No    

What sampling distribution will you use?

uniform normal     binomial chi-square Student's t

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

The level of significance is 0.05 H: The distributions are the same H: The distributions are different Observed Number Expected values E, = np! = 455 ( 0.072)-32.76 E. = np,-45510136-6188 E, = n = 455 (0.671) = 305.305 E4-np 4550.121)-55.055 Age (years) in the Village 48 Under 5 5 to 14 79 281 15 to 64 65 and older 47 EXCEL Mega Stat) output:

Goodness of Fit Test O-E 15.240 17.120 24.305 8.055 0.000 (0-E)" / E 7.090 4.736 1.935 1.179 14.940 %ofchis observed expected 32.760 61.880 305.305 55.055 455.000 48 79 281 47 455 47.46 31.70 12.95 7.89 100.00 14.94 chi-square 3 df 0019 p-value The value of the chi-square statistic for the sample is Yes, all the expected frequencies are greater than5 Chi-square test will be used Degrees of freedom 3 14.940 (c). P-value0.005

(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