In hypothesis testing, a p-value is used to determine whether the null hypothesis should be rejected. If the p-value is less than or equal to the significance level ($\alpha$), the result is considered statistically significant, meaning the null hypothesis is rejected.

Given that $\alpha = 0.02$:

• If p-value $\leq 0.02$, we reject the null hypothesis (statistically significant).
• If p-value $> 0.02$, we fail to reject the null hypothesis (not statistically significant).

Let's analyze the provided p-values:

1. 0.178 – This p-value is greater than 0.02. Thus, it does not imply statistical significance.
2. 0.014 – This p-value is less than 0.02. Thus, it implies statistical significance.
3. 0.004 – This p-value is less than 0.02. Thus, it implies statistical significance.
4. 0.01 – This p-value is less than 0.02. Thus, it implies statistical significance.

So, 0.178 does not imply statistical significance.

Would you like more details or have any questions?

Here are 5 related questions:

1. What does a p-value represent in hypothesis testing?
2. How is the significance level ($\alpha$) chosen in practice?
3. What are Type I and Type II errors in hypothesis testing?
4. How can you interpret results when the p-value is very close to $\alpha$?
5. What is the difference between one-tailed and two-tailed hypothesis tests?

Tip: Always report both the p-value and $\alpha$ to provide context for statistical significance.