Math Problem Statement

Find the critical​ value(s) and rejection​ region(s) for the type of​ z-test with level of significance

alphaα.

Include a graph with your answer.

RightRight​-tailed

​test,

alphaαequals=0.050.05

Question content area bottom

Part 1

The critical​ value(s) is/are

zequals=enter your response here.

​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

Solution

The graph above shows the standard normal distribution for a right-tailed z-test with a critical value z=1.645z = 1.645. The shaded area to the right represents the rejection region, where we reject the null hypothesis.

Would you like more details or have any questions?

Here are some related questions you might consider:

  1. How would the critical value change for a two-tailed test with α=0.05\alpha = 0.05?
  2. What is the rejection region for a left-tailed test with α=0.01\alpha = 0.01?
  3. How do you calculate the p-value for a right-tailed z-test?
  4. What happens if the test statistic falls outside the rejection region?
  5. How does changing α\alpha affect the critical value in hypothesis testing?

Tip: Always check whether you're dealing with a one-tailed or two-tailed test, as this significantly changes the critical value and rejection region.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Z-Test
Critical Value
Rejection Region

Formulas

Z = (X̄ - μ) / (σ/√n)
Critical Value for Right-Tailed Test at α = 0.05: Z = 1.645

Theorems

Standard Normal Distribution
Central Limit Theorem

Suitable Grade Level

Grades 10-12