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 . 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:
- How would the critical value change for a two-tailed test with ?
- What is the rejection region for a left-tailed test with ?
- How do you calculate the p-value for a right-tailed z-test?
- What happens if the test statistic falls outside the rejection region?
- How does changing 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
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