# MATH

bukysu

Chi-square distribution

Find the median of the chi-square distribution with 22degrees of freedom. Round your answer to at least two decimal places

In the question above the resolution had the equation of P(Xsquare > M)=0.5. Where did the 0.5 come from? Is it coming from the previous question answer?

## Chi-square distribution

Use the calculator provided to solve the following problems.
• Suppose that  follows a chi-square distribution with  degrees of freedom. Compute . Round your answer to at least three decimal places.

• Suppose again that  follows a chi-square distribution with  degrees of freedom. Find  such that . Round your answer to at least two decimal places.

• Find the median of the chi-square distribution with  degrees of freedom. Round your answer to at least two decimal places.

 Additional Resources Elementary Statistics (A Brief Version), 6th Ed.BlumanChapter 7: Confidence Intervals and Sample SizeSection 7.4: Confidence Intervals for Variances and Standard Deviations Supplementary Resources
• We're asked to compute , where  follows a chi-square distribution with  degrees of freedom. Using the calculator, we can compute  and use the complement rule to obtain :
 .
(Note that, since the degrees of freedom in the above calculation must be specified for the ALEKS calculator, the expression  appears as  with  in the calculator input.)

•  Figure 1

We are asked to find  such that  for a chi-square distribution with degrees of freedom. Note that such a  is the value that cuts off an area of  in the right tail of this distribution, that is,  for the distribution. See Figure 1, which depicts the distribution and an area of  shaded to the right of .

Using the calculator, we get

 .
(Note that we have to use the input  to specify the degrees of freedom.)

• We're asked to find the median of the chi-square distribution with  degrees of freedom. The median of a continuous distribution is the value that divides the distribution in half; in other words, the probability of obtaining a value greater than the median is  and the probability of obtaining a value less than the median is .
In finding the median of the chi-square distribution with  degrees of freedom, then, we are finding the value such that , where  follows a chi-square distribution with  degrees of freedom. In other words, we are finding  . Using the calculator, we get
 Comparing the mean and median of this distribution
.