Questions: Determine the critical values for the confidence interval for the population variance from the given values. Round your answers to three decimal places. n=17 and c=0.8.

Solution Steps

To determine the critical values for the confidence interval for the population variance, we need to use the chi-square distribution. The degrees of freedom (df) will be \( n - 1 \). We will find the critical values for the lower and upper tails of the chi-square distribution corresponding to the given confidence level \( c \).

Given \( n = 17 \), the degrees of freedom \( \text{df} \) is calculated as: \[ \text{df} = n - 1 = 17 - 1 = 16 \]

The confidence level \( c \) is given as \( 0.8 \). Therefore, the significance level \( \alpha \) is: \[ \alpha = 1 - c = 1 - 0.8 = 0.2 \]

Using the chi-square distribution, we find the critical values for the lower and upper tails corresponding to \( \alpha \).

The lower critical value is: \[ \chi^2_{\alpha/2, \text{df}} = \chi^2_{0.1, 16} \approx 9.312 \]

The upper critical value is: \[ \chi^2_{1-\alpha/2, \text{df}} = \chi^2_{0.9, 16} \approx 23.542 \]

Final Answer