Find the critical values for a 99% confidence interval using the chi-square distribution with 27 degrees of freedom. Round the answers to three decimal places. The critical values are ◻ and ◻.

Question

Find the critical values for a  99% confidence interval using the chi-square distribution with 27 degrees of freedom. Round the answers to three decimal places. The critical values are  ◻ and  ◻.

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Understand the problem: Understand the problem. We need to find the critical values for a 99% confidence interval using the chi-square distribution with 27 degrees of freedom. This means we are looking for the chi-square values that correspond to the lower and upper tails of the distribution, leaving 1% of the distribution outside the confidence interval (0.5% in each tail since it's a two-tailed test).Determine the alpha level: Determine the alpha level. Since we want a 99% confidence interval, the alpha level (α) is 1% or 0.01. This alpha level is split between the two tails of the chi-square distribution, so each tail will have an alpha level of 0.005.Find lower tail value: Find the critical chi-square value for the lower tail. Using a chi-square distribution table or calculator, we look up the value that corresponds to an area of 0.005 to the left (lower tail) for 27 degrees of freedom. This value is the lower critical value.Find upper tail value: Find the critical chi-square value for the upper tail. Similarly, we look up the value that corresponds to an area of 0.005 to the right (upper tail) for 27 degrees of freedom. This value is the upper critical value.Use chi-square calculator: Use a chi-square distribution calculator or table. Since the exact values are not provided in this format, we would typically use a chi-square distribution calculator or table to find the critical values. For 27 degrees of freedom and an alpha level of 0.005 in each tail, the critical values are approximately: Lower critical value (χ² lower): 13.121 Upper critical value (χ² upper): 44.314 These values should be rounded to three decimal places as per the problem statement.Round critical values: Round the critical values to three decimal places. Rounding the values obtained in Step 5, we get: Lower critical value (χ² lower): 13.121 → 13.121 (already at three decimal places) Upper critical value (χ² upper): 44.314 → 44.314 (already at three decimal places)

Find the critical values for a $99 \%$ confidence interval using the chi-square distribution with $27$ degrees of freedom. Round the answers to three decimal places. $\newline$ The critical values are $\square$ and $\square$ .

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Find the critical values for a 99% 99 \% 99% confidence interval using the chi-square distribution with 272727 degrees of freedom. Round the answers to three decimal places.\newlineThe critical values are □ \square □ and □ \square □.

Find the critical values for a $99 \%$ confidence interval using the chi-square distribution with $27$ degrees of freedom. Round the answers to three decimal places. $\newline$ The critical values are $\square$ and $\square$ .