In Exercises 3–8, find the critical value(s) and rejection reg...

Question

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Left-tailed test, α=0.10, n=38

Accepted Answer

Hello there. Today we're gonna 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. A production supervisor wants to test whether the average daily output of widgets exceeds 100 units. They plan a right tail T test at alpha equals 0.05 with a sample size of N equals 25. Determine its critical value and rejection region. Awesome. So it appears for this particular problem we're asked to solve for two separate answers. Our first answer is we're asked to determine the critical value, and our second answer, we're asked to determine what the rejection region is for this particular problem based on the information that is provided to us by the prom itself. So now that we know what we're trying to solve for, let's read off our final, let's read up, let's read off our multiple choice answers to see what our final answer might be, noting I'm gonna read the answer for the critical value first and the reject the null hypothesis if some condition T is less than or equal to, etc. So with that in mind, A is T subscript 0.95.25 is approximately equal to -1.708, and T is greater than -1.708. B is T subscript 0.95.25 is approximately equal to 1.708, and T is greater than 1.708. C is T subscript 0.05.24 is approximately equal to 1.711. And T is greater than 1.711. And finally, D is T subscript 0.05.24 is approximately equal to -1.711, and T is less than -1.711. Awesome. So first off, in order to solve this particular problem, we need to determine the degrees of freedom, which will denote as DF. And the degrees of freedom, as we should recall for this case, is equal to N minus 1, which will be equal to 25 minus 1, which is equal to 24. And now we need to test the type. So we're told that we're dealing with a right-tailed T test. So that means we test the mean if the mean, which will denote as mu, is greater than 100. So now we need to focus our attention on the critical value. So for a right tail test, as we should recall, at a significance level for this case, alpha is equal to 0.05, we need to solve for T subscript 0.05.24. Fantastic. So that will be our critical value. So we don't get confused, I'll call it say that it's equal to CV or critical value. So now we need to recall and use our T table or computer software, which you should have a T table in your textbook, and we will determine that T subscript 0.0524 will be approximately equal to 1.711. Which is one of our final answers. Hooray, we did it. We found our critical value. Now we need to determine the rejection region. So because our critical value is approximately equal to 1.711, therefore, without a doubt, the rejection region will be, we can reject the null hypothesis, you'll put an X next to age 0 because H0 denotes the null hypothesis. We can reject the null hypothesis. If T is greater than 1.711, and that is our second answer. All right, we did it. So looking at our multiple choice answers, the correct answer has to be multiple choice answer letter C, which once again is critical value T subscript 0.05.24 is approximately equal to 1.711. And reject H0 if T is greater than 1.711. And that's it. That is our final answer. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Left-tailed test, α=0.10, n=38

Key Concepts

Critical Value

Rejection Region

T-Test

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