Suppose the age distribution of the Canadian population and the age distribution of a random sample of 505 residents in the Indian community of Red Lake are shown below. $$\begin{array} { l l l }
\hline & & \text { Observed Number } \
\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \
\hline \text { Under } 5 & 8.5 \% & 45 \
5 \text { to } 14 & 10.4 \% & 50 \
15 \text { to } 64 & 68.2 \% & 367 \
65 \text { and older } & 12.9 \% & 43 \
\hline
\end{array}$$ Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Find the value of the chi-square statistic for the sample.
$$\alpha = 0.05$$
A)9.231
B)0.274
C)0.124
D)10.945
E)11.136

Question

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 505 residents in the Indian community of Red Lake are shown below. $$\begin{array} { l l l } 
\hline & & \text { Observed Number } \
\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \
\hline \text { Under } 5 & 8.5 \% & 45 \
5 \text { to } 14 & 10.4 \% & 50 \
15 \text { to } 64 & 68.2 \% & 367 \
65 \text { and older } & 12.9 \% & 43 \
\hline
\end{array}$$ Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Find the value of the chi-square statistic for the sample.
$$\alpha = 0.05$$
A)9.231
B)0.274
C)0.124
D)10.945
E)11.136

Quizplus · Accepted Answer

To find the chi-square statistic, we first calculate the expected number of residents in each age group based on the percentages of the Canadian population, then apply the formula for the chi-square statistic: $\chi^2 = \sum \frac{(O - E)^2}{E}$, where $O$ is the observed frequency and $E$ is the expected frequency.1. Calculate expected frequencies (E) for each age group:   - Under 5: $505 \times 0.085 = 42.925$   - 5 to 14: $505 \times 0.104 = 52.52$   - 15 to 64: $505 \times 0.682 = 344.41$   - 65 and older: $505 \times 0.129 = 65.145$2. Calculate $\chi^2$ using the formula:   - Under 5: $\frac{(45 - 42.925)^2}{42.925} = 0.100$   - 5 to 14: $\frac{(50 - 52.52)^2}{52.52} = 0.121$   - 15 to 64: $\frac{(367 - 344.41)^2}{344.41} = 1.804$   - 65 and older: $\frac{(43 - 65.145)^2}{65.145} = 7.206$3. Sum the values: $0.100 + 0.121 + 1.804 + 7.206 = 9.231$Therefore, the chi-square statistic for the sample is 9.231.

Suppose the Age Distribution of the Canadian Population and the Age