The p-value for a hypothesis test turns out to be 0.06565. At a 2% level of significance, what is the proper decision?

Reject H0

Fail to reject

At a 2% level of significance, you compare the p-value with the significance level (α = 0.02) to make the decision.

- **If the p-value is less than α (0.02),** you reject the null hypothesis (H₀).
- **If the p-value is greater than α (0.02),** you fail to reject the null hypothesis (H₀).

In this case, the p-value is **0.06565**, which is **greater** than 0.02.

**Therefore, the proper decision is:**
**Fail to reject H₀.**

Would you like more details on hypothesis testing? 

Here are some related questions:
1. What is the definition of a p-value in hypothesis testing?
2. How do you interpret the result of a hypothesis test when the p-value is greater than the significance level?
3. What is the difference between one-tailed and two-tailed hypothesis tests?
4. How does the choice of significance level (α) affect the decision in hypothesis testing?
5. What are Type I and Type II errors in hypothesis testing?

**Tip:** The p-value represents the probability of observing the data (or something more extreme) if the null hypothesis is true. It helps you assess whether there is enough evidence to reject H₀.

The p-value for a hypothesis test turns out to be 0.06565. At a 2% level of significance, what is the proper decision?

Learn how to make decisions in hypothesis testing by comparing the p-value with the significance level. This problem demonstrates the steps to take when the p-value is 0.06565 and the significance level is 2%. Suitable for students in Grades 11-12.

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