Math Problem Statement
Solution
The problem presented involves a comparison between the p-value of a hypothesis test and the significance level (denoted by ).
- The significance level () is 1%, which is .
- The p-value from the test is .
In hypothesis testing, we reject the null hypothesis when the p-value is less than or equal to the significance level.
Step-by-step analysis:
- The given p-value is less than the significance level .
- Therefore, is the correct comparison.
Thus, in the illustration provided:
- The first box is incorrect as the p-value is not equal to the significance level.
- The second box correctly shows that .
Would you like more details on hypothesis testing and p-values? Here are five related questions:
- What does it mean to reject the null hypothesis in this context?
- How does the significance level affect the outcome of a hypothesis test?
- What are Type I and Type II errors in hypothesis testing?
- How is the p-value calculated in a hypothesis test?
- What happens if the p-value equals the significance level exactly?
Tip: Always compare the p-value to the significance level to determine if the result is statistically significant.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Significance Level
P-Value
Formulas
p-value < α
Theorems
Null Hypothesis
Significance Testing
Suitable Grade Level
Undergraduate or Advanced High School Statistics
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