Finding Critical Values and Rejection Regions In Exercises 23–...

Question

Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.

Two-tailed test, α = 0.12

Two-tailed test, α = 0.12

Accepted Answer

Hello everyone. Let's take a look at this question together. Find the critical values and rejection regions for a two-tailed Z test where alpha equals 0.022. So in order to solve this question, we have to recall how to find critical values and a rejection region so that we can find both for a two-tailed Z test where our alpha is equal to 0.022. And we know that for a two-tailed Z test, we divide the given alpha by 2 to get the area of each tail. So, 0.022, divided by 2 is equal to 0.011. So the area of each tail is 0.011, and then we will let Z1 be the critical value in the lower tail, and Z2 be the critical value in the upper tail. And then we find the Z score corresponding to a cumulative probability of 0.011 in the lower tail, which using the standard normal distribution table, For the probability of Z being less than Z1 equaling 0.011, our Z1 value is equal to -2.29. And since the standard normal distribution is symmetrical, we can conclude that for the upper tail, which is the probability of Z being greater than our second critical value equaling 0.011, our Value for Z2 is equal to 2.29. Therefore, the critical values are for Z1, we have 2.29, and for Z2, we have 2.29. And now we have to find the rejection regions for this two-tailed test, which we know the rejection regions for a two-tailed Z test are given as the following to the Left of the critical value in the lower tail and also to the right of the critical value in the upper tail. Therefore, the rejection regions are Z is less than -2.29 or Z is greater than 2.29. And based on our calculations, we know that the critical values are critical value 1 is equal to -2. 29, and critical value 2 is equal to 2.29, and our rejection regions are Z is less than -2.29 or Z is greater than 2.29. And looking at our answer choices, we can identify that this matches answer choice B, so answer choice B is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.

Two-tailed test, α = 0.12

Key Concepts

Critical Value

Rejection Region

Two-Tailed Test

Watch next

Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.Two-tailed test, α = 0.12

Key Concepts

Critical Value

Rejection Region

Two-Tailed Test

Watch next

Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.

Two-tailed test, α = 0.12