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 = 0.99, n = 30

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says to find the critical values, chi squad sub R and chi squadL or a 98% confidence level, and a sample size of 25. Now, in order to find our critical values, we'll first need to find the number of degrees of freedom. And recall that our degrees of freedom, which we'll label as DF, is equal to N minus 1, where in here is our sample size. Now we're given a sample size of 25 in the problem, so that means our degrees of freedom is going to be equal to 25 minus 1, which is going to be equal to 24. Now, the other piece of information that we need is the area underneath the tails, so the area that is outside of our 98% confidence level in the tails. And for a 98% confidence level, that area is going to be 1 minus 0.98, which is equal to 0.02. So that's the area underneath the tails on both the left and the right side. And we actually are interested in just the area underneath one of those tails. So we'll take this value and divide it by 2. So we'll have 0.02. Divided by 2, which is going to be equal to 0.01. So our chi squared sub L will correspond to the left tail value, where the area to the left is 0.01, and our chi squared subR is going to correspond to the right tail value, where the area to the left is 0.99, which is just 1 minus 0.01. And so, to find these values, we'll just need to look them up with a chi squared distribution table or using a calculator. So, for chi squared sub L, that is going to be equal to chi2 with an area of 0.01 to the left and 24 degrees of freedom, and when we look up this value in our table, this is going to be equal to. 11.091. And our chi squared sub R is going to be equal to chi2 value for our table with an area of 0.99 to the left. And 24 degrees of freedom, and when we look up this value in our table, we get. 10.856. So, these are actually the answers that we're looking for, for this problem. So I hope that this explanation has been useful, and I'll see you 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 = 0.99, n = 30

Key Concepts

Chi-Square Distribution

Critical Values

Level of Confidence

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