For a random sample of 23 European countries, the variance on life expectancy was years. What is the 95% confidence interval for the variance of life expectancy in all of
Europe?
A) $4.4

Question

For a random sample of 23 European countries, the variance on life expectancy was years. What is the 95% confidence interval for the variance of life expectancy in all of
Europe? 
A) $4.4 < \sigma ^ { 2 } < 14.6$
B) $5.6 < \sigma ^ { 2 } < 10.3$
C) $27.2 < \sigma ^ { 2 } < 118.3$
D) $28.9 < \sigma ^ { 2 } < 115.0$

Quizplus · Accepted Answer

The 95% confidence interval for the variance of life expectancy in all of Europe is given by:$$\chi^2_{0.025,22} < \frac{(n-1)s^2}{\sigma^2} < \chi^2_{0.975,22}$$where $\chi^2_{0.025,22}$ and $\chi^2_{0.975,22}$ are the 2.5th and 97.5th percentiles of the chi-squared distribution with 22 degrees of freedom, respectively.Using a chi-squared distribution table, we find that $\chi^2_{0.025,22} = 10.982$ and $\chi^2_{0.975,22} = 35.532$.Therefore, the 95% confidence interval for the variance of life expectancy in all of Europe is:$$10.982 < \frac{(23-1)s^2}{\sigma^2} < 35.532$$$$\Rightarrow 4.4 < \sigma ^ { 2 } < 14.6$$

For a Random Sample of 23 European Countries, the Variance 4.4<σ2<14.64.4 < \sigma ^ { 2 } < 14.64.4<σ2<14.6

For a Random Sample of 23 European Countries, the Variance $4.4 < \sigma ^ { 2 } < 14.6$