If you have a hypothesis test with alpha = 0.02, which of the following P-Values does NOT imply statistical significance?
0.178
0.014
0.004
0.01

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.

If you have a hypothesis test with alpha = 0.02, which of the following P-Values does NOT imply statistical significance? 0.178, 0.014, 0.004, 0.01

Explore how to interpret p-values in hypothesis testing with a significance level of α = 0.02. Learn when to reject the null hypothesis based on the p-value, with examples like p-values of 0.178, 0.014, 0.004, and 0.01. Suitable for undergraduate-level statistics.

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