Math Problem Statement
Solution
To find the p-value for a two-tailed test with a given -score of :
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First, find the probability associated with on a standard normal distribution (this is the area to the left of ).
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For , the left-tail probability is approximately 0.0021.
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Since this is a two-tailed test, we double this probability:
Answer: The p-value to four decimal places is .
Would you like a detailed explanation of each step, or do you have any questions?
Here are 5 related questions for further exploration:
- How would the p-value change if this were a one-tailed test instead?
- What does a p-value of 0.0042 imply about the null hypothesis in a hypothesis test?
- How do you interpret a negative -score in the context of hypothesis testing?
- How does changing the significance level affect the conclusions drawn from this p-value?
- Can you calculate the p-value if the -score were (positive) instead?
Tip: In two-tailed tests, always remember to double the tail probability to get the p-value.
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Math Problem Analysis
Mathematical Concepts
Statistics
Hypothesis Testing
Standard Normal Distribution
Two-Tailed Test
Formulas
P-value for a two-tailed test: p = 2 * P(Z < z)
Theorems
Properties of the Standard Normal Distribution
Suitable Grade Level
Grades 11-12
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