The p-value of the test is 0.028. What is the decision of the test?

The decision of a hypothesis test based on the p-value depends on the significance level (α) chosen for the test. The significance level represents the threshold below which we reject the null hypothesis.

Given:
- **p-value** = 0.028

### Steps to determine the decision:
1. **Compare the p-value to the significance level (α)**:
   - If **p-value ≤ α**, reject the null hypothesis \( H_0 \).
   - If **p-value > α**, fail to reject the null hypothesis \( H_0 \).

For example, if the commonly used significance level **α = 0.05**, then:
- Since 0.028 is less than 0.05, we reject the null hypothesis.

If the significance level **α = 0.01**, then:
- Since 0.028 is greater than 0.01, we fail to reject the null hypothesis.

### Conclusion:
- If \( α = 0.05 \), **reject** the null hypothesis.
- If \( α = 0.01 \), **fail to reject** the null hypothesis.

Do you know the significance level, or would you like more details?

### Related Questions:
1. What is the null hypothesis in this context?
2. How does changing the significance level affect the decision?
3. What are Type I and Type II errors in hypothesis testing?
4. How do you calculate a p-value?
5. Can the p-value tell you the strength of the evidence?

**Tip**: The p-value does not tell you the probability that the null hypothesis is true, but rather how consistent the data is with the null hypothesis.

Discover how to interpret a p-value of 0.028 in a hypothesis test. Learn about hypothesis testing concepts, the role of significance levels, and how the p-value helps you decide whether to reject the null hypothesis. Suitable for undergraduate statistics students.

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