A 99% confidence interval for population variance is being formulated based on a sample of 16 observations. What are appropriate values for X^2
Find chi-square values by using a chi-square table for the 99% interval. Use n-1 for degrees of freedom (n = sample size).
To find the appropriate value for X^2 (chi-square) for a 99% confidence interval for population variance, you need to consider the degrees of freedom.
Since you have a sample of 16 observations, the degrees of freedom for the sample variance is determined by n-1, where n is the sample size. In this case, the degrees of freedom will be 16 - 1 = 15.
To find the appropriate value of X^2 for a 99% confidence interval, you need to consult a chi-square distribution table or use a statistical software.
For a 99% confidence interval with 15 degrees of freedom, you need to find the chi-square value that accumulates 99% of the area under the curve to the right. This value corresponds to the critical chi-square value, denoted as X^2(0.01, 15).
Using a chi-square distribution table or statistical software, you can find that the value of X^2(0.01, 15) is approximately 33.924.
Therefore, for a 99% confidence interval for population variance based on a sample of 16 observations, the appropriate value for X^2 is 33.924.