The age distibution of the Canadian population and the age distribution of a ran

Question

The age distibution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of Red Lake Village are shown below.

Use a 5% level of signigicance 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 alternative hypothesis.

b) find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? what sampling distibution will you use? What are the degrees of freedom?

c) find the P-value

d) based on your answers a-c will you reject or fail to reject the null hypothesis of independence?

e) your conclusion.

Please show ALL work.

Age Percent of Canadian population Observed number in Red Lake Village Under 5 7.2% 47 5-14 13.6% 75 15-64 67.1% 288 65 and older 12.1% 45

Explanation / Answer

Alpha = 0.05

H0: t the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village

Ha: does not fit

Two tailed test

yes. freq >5. chi square test is used

The P-Value is 0.008146. The result is significant at p < 0.05.

Reject null hypothesis.

the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village is not statistically evident.

Age Percent of Canadian population Observed number in Red Lake Village Expected chi square Under 5 7.20% 47 32.76 6.189792 14-May 13.60% 75 61.88 2.781745 15-64 67.10% 288 305.305 0.980865 65 and older 12.10% 45 55.055 1.8364 Total 100.00% 455 455 11.7888 df 3

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