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.