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.

Right-tailed test, n=27,α=0.05

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In a fatigue test of steel rods, engineers want to know if the variability in breaking strength exceeds the industry standard. They test a random sample of 15 rods and perform a right-tailed G squared test at alpha equals 0.01, give its critical value and rejection region. Awesome. So we're told. To give its critical value and rejection region. So we're asked to solve for the critical value and the rejection region for this particular prompt, and those are our final two answers we're ultimately trying to solve for. So with that in mind, let's read off our multiple choice answers to see what our final answer might be, noting that I will read the value for the critical value first. And then I'll read the value for the rejection region, knowing that the critical value states that Chi subscript 0.01.142 is approximately equal to some value. And for the rejection region, it says it will state reject H0 if some expression. So A will be 26.22 and T squared is greater than 26.22. B is 29.01, and T squared is greater than 29.01. C is 29.14 and T squared is greater than 29.14. And D is 30.58 and she squared is greater than 30.58. Awesome. So our first step that we need to take in order to solve this particular problem is we need to determine the degrees of freedom, which, as we should recall, DF, the degrees of freedom, is equal to N minus 1, which in this case it's equal to 15 minus 1, which is equal to 14. Awesome is we're told that the random sample is 15 rots. Moving right along here. So as we should recall, since we are checking to see if variance exceeds the standard, we will need to perform a right tail test at the significance level alpha equals 0.01. And once again, we need to note that we're dealing with a right tail test which we'll call RT for short. So we now need to determine the critical value at a significance level of 0.01, and we're also told that the degrees of freedom is 14. So that will mean that our critical value, which you'll call CV for short, will be approximately equal to 29.14. So therefore, without a doubt, the rejection region will be, we can reject the null hypothesis, which will denote as H 0, so we can reject the null hypothesis if T2 is greater than 29.14. So that will mean that our final answer. Without a doubt, will have to be multiple choice answer letter C, which states once again the critical value. A so Chi subscript 0.01.142 is approximately equal to 29.14, and the rejection region reject H0 if Tsquared is greater than 29.14. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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.

Right-tailed test, n=27,α=0.05

Key Concepts

Chi-Square Test

Critical Value

Rejection Region

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