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 = 15

Accepted Answer

Hi, everybody. Welcome back. Our next problem says find the critical values. For chi squared on the right and the left for a confidence level of C equals 0.90 and a sample size of N equals 19. So, we're looking for both right and left tailed critical values. So, this will be a two-tailed. Test So we need to remember that we're going to look at the areas on. Both sides of the distribution. So our confidence level is 0.90, it means we have alpha equals 0.10. 1 minus C is alpha. And then what we need to continue consider is that the area. In each tail is actually equal to. Alpha divided by 2. So, we're going to consider that area as our alpha value when calculating our chi squared critical values. For a chi square calculation we need degrees of freedom. So that will be. The sample size N minus 1, we're told the N is 19, so in this case our degrees of freedom are 18. So since our high squared table is usually presented as a right-sided table, it's easier to start with our right. Cited chi square critical value. So, we'll calculate that, and we're going to look at the chi square table based on, remember, we need to look at alpha divided by 2. So, we're going to call that 0.05. So, that would be our alpha on the table, for purposes of the table, with 18 degrees of freedom. And that gives us 28. 0.869. And then recall we need one extra step for the left sided critical value, because of the way the table is designed. We then Use as alpha for the left side, that's right, chi squared to the left. We'll say alpha equals 1 minus 0.05. Which equals 0.95. Sounds like an 8. We'll say for the left side. That's because again, since we're given a right sided table, we're looking at the situation where. 95% or the probability is not 0.95, that the value will fall on the right side of that left critical value. And then what's left on the left side of our critical value will be 0.05, or our area in the left side tail. So, using that 0.95 value and then 18 degrees of freedom, that gives us a left sided critical chi squared value of 9.390. So, there we go. We were asked to find the right-sided and left-sided critical values for chi squared, with a confidence level of C equals 0.90, and a sample size of 19. And we get. A result of our right-sided chi squared critical value is 28.869. And our left-sided critical chi square value is 9.390. 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 = 15

Key Concepts

Chi-Square Distribution

Critical Values

Degrees of Freedom

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