Math Problem Statement

A hypothesis test is conducted at the 1% significance level. The test yields a p-value of 0.004. Compare the level of significance and the p-value.

Solution

The problem presented involves a comparison between the p-value of a hypothesis test and the significance level (denoted by α\alpha).

  • The significance level (α\alpha) is 1%, which is 0.010.01.
  • The p-value from the test is 0.0040.004.

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:

  1. The given p-value 0.0040.004 is less than the significance level 0.010.01.
  2. Therefore, p-value<α\text{p-value} < \alpha 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 p-value<α\text{p-value} < \alpha.

Would you like more details on hypothesis testing and p-values? Here are five related questions:

  1. What does it mean to reject the null hypothesis in this context?
  2. How does the significance level affect the outcome of a hypothesis test?
  3. What are Type I and Type II errors in hypothesis testing?
  4. How is the p-value calculated in a hypothesis test?
  5. 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