Final answer:
The x2 left and x2 right for a 99% confidence interval with 20 degrees of freedom in the chi-square distribution represent the critical values that border the central 99% of the distribution.
These values can be found in a chi-square table or calculated using a statistical calculator or software with the respective cumulative probabilities of 0.005 and 0.995.
Step-by-step explanation:
To find x2 left and x2 right for a 99% confidence interval using the chi-square distribution with 20 degrees of freedom, you will need to refer to a chi-square distribution table or use a statistical calculator.
The values correspond to the critical values which encompass the central 99% of the chi-square distribution with 20 degrees of freedom.
The chi-square distribution is not symmetric, and hence the critical values on the left and right differ. To find these values, you need to know the cumulative probabilities on each end. For a 99% confidence interval, there is 0.5% in each tail of the distribution (because 100% - 99% = 1% and 1% / 2 = 0.5%).
Thus, you are looking for the chi-square value where 0.5% of the distribution lies above it (x2 right) and the chi-square value where 0.5% of the distribution lies below it (x2 left).
To find the x2 left, you would look up or calculate the 0.005 cumulative probability point for 20 degrees of freedom. Similarly, for x2 right, you would look up or calculate the 0.995 cumulative probability point for 20 degrees of freedom.
Values for x2 left and x2 right can usually be found directly in chi-square tables or calculated using functions in statistical software.
For example, in many statistical software packages, you can use the qchisq function, specifying the probabilities and degrees of freedom to obtain these critical values.