In Exercises 13–16, find the critical value(s) and rejection r...

Question

In Exercises 13–16, find the critical value(s) and rejection region(s) for the type of z-test with level of significance . Include a graph with your answer.

Two-tailed test, α=0.03

Accepted Answer

Hello everyone, glad to have you back. The next problem says. Determine the critical value or values, and rejection region or regions for a two-tailed Z test with alpha equals 0.08. So, we're looking for, we have two regions here. Both With a critical Z value. So, we're going to have a positive Zval critical and a negative critical Z value. And our rejection region will be that area under the curve to the left of our negative critical Z value. And to the right of our positive critical C. Value. So, 2 rejection regions. Objection Region Since we have a two-tailed test. And note that we're given alpha, which is an area, but because we have two parts to this, each rejection region. Has an area of alpha divided by 2. So, when we have an area, when we have a P value, we can find a Z value from our Z table. We're going to need to take into account that we have these two areas we're looking for, two critical Z values, but We can look up these regions and recall that the area in our Z tables refers to the area to the left of our Z value. So, the simplest way to do it is look for the negative Z value. So, we have alpha 0.08, alpha over 2 is 0.04. And we're going to use this. As the P value, In the Z table. So you can either use your calculator or look this up on a Z table. Pause the video if you want to look at your table. And the negative Z value, so that's where we want to look at the negative Z value in this case, from the table will be -1.75 approximately. Not exactly. So, we know that we have two critical values, so we'll say Z sub C are critical values, are going to equal -1.75, so that will be on the left side. And positive. 1.75 on the right side. And in our rejection regions. Will be those areas where the probability, so the area under the curve, is smaller than alpha. So again, we'll have two rejection regions here on the left and on the right. So, the rejection region on the left will be where Z value from our test. is less than 1.75, and You say or so we'll reject our hypothesis if Z is less than 0.575. -1.75. Goodness, having trouble with that one. Or where Z is greater than 1.75. So there we go, we have our two-tailed Z test. And we calculated our two critical values, negative and positive 1.75. And our two rejection regions will reject our hypothesis when Z is less than -1.75, or if Z is greater than 1.05. See you in the next video.

In Exercises 13–16, find the critical value(s) and rejection region(s) for the type of z-test with level of significance . Include a graph with your answer.

Two-tailed test, α=0.03

Key Concepts

Critical Value

Rejection Region

Z-Test

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