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 = 0.95, n = 20

Accepted Answer

Hello everybody. Glad to have you back with us. We will take a look at this next problem. Determine the critical values. We have a chi squared right-sided critical value, and chi squared left-sided critical value for a confidence level of C equals 0.90, and a sample size of N equals 12. So to find these chi squared critical values, we know we'll need degrees of freedom, or DF. Which equals sample size minus 1 or N minus 1. We have an N of 12, so our degrees of freedom equals 11. And then if our confidence level is 0.90. Then our alpha will equal 1 minus 0.90. So equals 0.10. Now, we are finding both the left and right side of critical values. So in that case, we need to look at the areas of the tails on both sides. And so the area in each tail. It's going to equal alpha divided by 2, so that will equal 0.05. Now note that even though our significance level of alpha here is 0.1. For the sake of looking it up in the table, we will treat that 0.05 as the alpha for our right-sided critical value. But remember that it actually means the area under the tail. So, our right sided critical value is pretty straightforward, since chi squared tables are right-sided in general. In that they give you the probability. Of a value falling to the right side of that critical value in the distribution. So, our right-sided critical value here, we use that 0.05 as our alpha, with 11 degrees of freedom, and that's going to give us the right-sided value of 19 675 For the left-sided critical value, we need to calculate. R alpha for the purposes of the table. By subtracting, we'll say for a left side. Critical value. We're going to say that probability is equal to 1 minus 0.05. And that will equal 0.95. And we're going to look that up using that as our probability or our alpha. So again, this reflects the pro when 95% of the values are going to fall to the right side of that critical value. So are Left-sided critical value. If we look it up on the table with 0.95 and then 11 degrees of freedom, that's going to give you as a value of 4.575. And we could check that that makes logical sense, because our right-sided value should obviously be much larger than our left sided volume. So, once again, we needed the right-sided and left-sided chi squared critical values, with a confidence level of 0.90, and a sample size of 12, and that gives us a right-sided critical value of 19.675, and a left-sided critical value of 4.575. 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 = 0.95, n = 20

Key Concepts

Chi-Squared Distribution

Critical Values

Degrees of Freedom

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