Finding Critical Values for χ2 In Exercises 3–8, find the crit...

Question

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.80, n = 51

Accepted Answer

Hello. In this video, we are given a confidence level of 0.90 and a sample size of 16. We want to determine the critical values of the endpoints for the chi square distribution. So just to list out the given information, we are working with a confidence level of 0.90, and we have a sample size of 16. Now, the first thing we want to do is you want to go ahead and determine the degree of freedom for the critical values. The degree of freedom is defined as our sample size minus 1. That is going to be 16 minus 1, which is going to give us a degree of freedom of 15. Now, for the chi square distribution, what we want to find is the area under the tail ends of the distribution. Now for the confidence level, we are 90% confident that we are going to be in the middle of the distribution, but in order to find the areas of the tail ends, we need to find the area of the complement of the confidence level. That is going to be 1 minus 0.90, which is going to give us 0.10. This tells us that the total area of the sum of the endpoints is going to be 0.10, but since we are working with two endpoints, we need to divide this total area by 2. 0.10 divided by 2 is going to be 0.05. So, now what we need to do is we need to determine the left and right endpoints or the areas for the critical values. Now, this is telling us that the left area is going to be 0.05, but for the uppermost area for chi squared sub R, that area is going to be 0.05 complemented of 90, 0.90, and that is going to be 0.95. So, we will define chi squared R. To be chi squared. Sub 0.95 with respect to the degree of freedom which is 15, and we will define the left end point chi squad subl as chi square 0.05 with respect to our degree of freedom, which is 15. Now, by using a chi square table, we can find the critical values for this distribution. For the left end point, by using the table, we get a critical value of 7.261. And by using the table, we get a right most critical value of 24. 996, and these are going to be the critical values for the left and right endpoints of the chi squared distribution, and the solution to this problem is going to be C. So, I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.
c = 0.80, n = 51

Key Concepts

Chi-Square Distribution

Critical Values

Degrees of Freedom

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