In Exercises 7–12, find the critical value(s) and rejection re...

Question

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Left-tailed test, n=24,α=0.05

Accepted Answer

Welcome back, everybody. Our next question says, for a left-tailed chi square test with sample size N equals 18, and significance level alpha equals 0.01, what is the critical value and the rejection region? So, let's recall that a left-tailed chi square test is just a little bit tricky, needs one extra step. So, to use our table, just as with the right right tail chi square test, we need our degrees of freedom, which we can recall equals the sample size N minus 1. In this case, our sample size is 18, so degrees of freedom equals 17. And then we need Our significance level. However, unlike with normal distributions, where our critical values, our distribution is symmetrical, so our critical values will be the positive and negative values on either side. With a T Sorry, for the chi square distribution, we are not symmetrical and so for the left tailed test, it's useful to sketch out a diagram. If we imagine our. Chi square distribution. And we're looking for the left side, such that the area under the left tail is going to be less than 0.01. So, we'll draw a line for our critical value, obviously pretty close to the left side here. So, there's our critical value, and we know what we're looking for, and I will highlight that in yellow to indicate it's our answer. Is this area to the left. Now, recall that the bear chi square table is listed. It lists everything in the form of a right-tailed the test. So, We would look at, we're looking for the critical value at which, so. If we need to look for. The Number that goes with the right side, everything to the under the curve to the right side of the critical value. We know the probability under this curve, so that blue highlighted area. Must be 1 minus 0.01. So it will equal 0.99. So there's a 99% probability that the value will lie to that right side, leaving 0.01 R alpha. As that yellow highlighted area on the left side. So, it's a simple calculation, but you always, it's always helpful to sketch this out and think about what you need, and we need a left tailed chi square test, so we need to take that extra step. So, we're going to treat from our table, our alpha in this case as 0.99. So we've got degrees of freedom, and we've got alpha. So we just use this value on our chi square table, and look that up. And that will give us the critical value. And from the table that will equal 6.408. Now the other thing we're asked for is the rejection reason. So we will reject our null hypothesis when we're looking at the left tail. When our chi square value is less than our critical value, since it's left tailed, so when chi squared, oops, you in the wrong place, chi squared is less than 6.408. So, again, we were asked for critical volume and rejection reason for a left-tailed chi square test. We have N equals 18 and alpha equals 0.01. And we get a critical value of 6.408, and we reject our null hypothesis, when chi squared is less than that critical value of 6.408. See you in the next video.

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Left-tailed test, n=24,α=0.05

Key Concepts

Chi-Square Test

Critical Value

Rejection Region

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