A sample of 21 elements is selected to estimate a 90% confidence interval for the variance of the population. The chi-square value(s) to be used for this interval estimation is(are)
A) 31.410.
B) 12.443.
C) 10.851 and 31.410.
D) 12.443 and 28.412.

Question

Quizplus · Accepted Answer

To estimate the confidence interval for the variance of the population, we use the chi-square distribution. The degrees of freedom for this distribution is equal to the sample size minus one, which for this case is 21 - 1 = 20.

To find the chi-square value(s) to be used for a 90% confidence interval, we need to look up the values of chi-square with 20 degrees of freedom in a chi-square distribution table. The value for the upper tail probability of 0.05 (since it's a two-tailed test and 0.1 is divided among two tails) is 31.410, and the value for the lower tail probability of 0.05 is 10.851.

Therefore, the chi-square values to be used for this interval estimation are 10.851 and 31.410. Choice C is the only option that includes both values.

A Sample of 21 Elements Is Selected to Estimate a 90