5. Suppose the age distribution of the Canadian population and the age distribut

Question

5. Suppose the age distribution of the Canadian population and the age distribution of a random sample of 452 residents in the Indian community of Red Lake are shown below. Observed Number Percent of Canadian Population 12.5% 10.1% in Red Lake Village Age (years) Under 5 5 to 14 15 to 64 69.9% 65 and older 50 45 313 Use = 0. 05 to test the claim that the age distribution of the general Canadian population fits the age test distribution of the residents of Red Lake Village. Find (or estimate) the P-value of the sample statistic A) P-Value>0.50 B) 0.25 P-Value

Explanation / Answer

First we can state the hypothesis as below:
H0: The distribution of the ages in the Indian community of Red Lake Village is the same as in the rest of Canada
HA: The distribution of the ages in the Indian community of Red Lake Village is different from the rest of Canada
at the 5% significance level

Chi-square Goodness-of- fit Test if the conditions are met
RANDOM: stated random sample of 452 residents
INDEPENDENT: There are more than 10(452) = 4520 residents in the community
LARGE SAMPLE SIZE: all expected counts are at least 5

Under 5 - Observed count:50, Expected count:452(.075)=33.9
5 to 14 - Observed count:45, Expected count:452(.125)=56.5
15 to 64 - Observed count:313, Expected count:452(.699)=315.948
65 and older - Observed count:44 , Expected count:452(.101)=45.652

(50-33.9)^2/33.9 + (45-56.5)^2/56.5 + (313-315.948)^2/315.948 + (44-45.652)^2/44 = 10.07655

degrees of freedom - 4 - 1 = 3

From the chi square calculator, we can find the p value which is (1 - 0.98) = 0.02

Since the P-value of 0.02 < 0.05. we Reject H0. There is sufficient evidence to support the claim that the distribution of ages in the Indian community of Red Lake Village is different from the rest of Canada.

So option E is correct.

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