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=20

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 sleep researcher is testing whether a new mattress reduces average sleep time compared to the national average. She decides to perform a left tail tea test at the 0.10 level of significance using data from a random sample of 20 people. What is the critical value and rejection region for this T test? 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 what is the critical value. That's our first answer. And our second answer is what is the rejection region for this T test, and that is our second answer. So now once again that we now know we're ultimately trying to solve for the critical value and the rejection region for this particular T test. Our first step that we must take is we need to identify the degrees of freedom, but before we do that, let us write down all of our known variables. And let us also quickly recap that we are asked to find the critical value and the the rejection region for a left tail T test using the following information that alpha, which denotes the level of significance, and alpha in this case is equal to 0.10, and we're also told that the sample size, which will denote as N is equal to 20. So once again we need to use our level of significance and our sample size to help us determine the degrees of freedom. So now that we know that we're trying to determine the degrees of freedom, we need to recall a note that for a one sample T test, the degrees of freedom are DF, as we should recall. So DF is equal to N minus 1, which is equal to when we plug in our known variables, 20 minus 1, which is equal to 19. Fantastic. Our second step now is we need to recall and use the T distribution table. So when we look up the criticalt value for a left tail test at a significance of alpha equals 0.10 using our T distribution table in our textbook. Noting that once again that our degrees of freedom, DF is equal to 19, we will find that TC, our critical T value, is equal to -1.328. And once again, this is when you use your T distribution table, which should be table 5 in your elementary statistics textbook 8th edition. And we need to note once again that T values for left tail tests are negative, so that's very important to recall. So I'll say it again. T values for left tail tests are negative. So moving right along here, our third step is we need to state the rejection region. And the rejection region for a left-tailed T test, the rejection region will be that T. is less than -1.328. And we also need to recall and note that if the calculated test statistic falls in this particular region, we would reject the null hypothesis. So that will mean that our final two answers, without a doubt, so we're told that our critical value. Once again, our critical value TC is equal to -1.328, and our rejection region is T is less than -1.328. And to quickly summarize, once again, our final two answers once again without a doubt our critical value is -1.328. And the rejection region is T is less than -1.328, and that's it. Those are our final two answers. 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=20

Key Concepts

Critical Value

Rejection Region

T-Test

Watch next