What would be the result of a hypothesis test where test-statistic=2.23, p-value=0.0339 and α=.01?

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6VC. Hypothesis test example, population standard deviationLinks to an external site. (3:35)

6DG. P values and alphaLinks to an external site.Open this document with ReadSpeaker docReader  (DOCX)

Group of answer choices

Reject Ho since p-value is not less than α

Reject Ho since p-value is less than α

Do not reject Ho since p-value is not less than α 

Do not reject Ho since p-value is less than α

To determine the result of the hypothesis test, we compare the p-value to the significance level (\(\alpha\)).

- **Given:**
  - Test statistic = 2.23
  - p-value = 0.0339
  - \(\alpha = 0.01\)

**Decision Rule:**
- If the p-value is less than \(\alpha\), reject the null hypothesis (\(H_0\)).
- If the p-value is greater than or equal to \(\alpha\), do not reject the null hypothesis (\(H_0\)).

**Comparison:**
- p-value (0.0339) is **greater** than \(\alpha\) (0.01).

**Conclusion:**
- Since the p-value is not less than \(\alpha\), we **do not reject** the null hypothesis (\(H_0\)).

So, the correct answer is:

**Do not reject Ho since p-value is not less than α.**

Would you like more details or have any questions?

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Here are 5 related questions you might find useful:

1. What does it mean to reject the null hypothesis?
2. How do you interpret the p-value in hypothesis testing?
3. What are Type I and Type II errors in hypothesis testing?
4. How is the significance level (\(\alpha\)) chosen in a hypothesis test?
5. What are the implications of not rejecting the null hypothesis?

**Tip:** Always compare the p-value with the significance level (\(\alpha\)) to make the correct decision in hypothesis testing.

Explore an example of hypothesis testing where the test statistic is 2.23, the p-value is 0.0339, and the significance level is α = 0.01. Learn how to interpret the results and decide whether to reject the null hypothesis based on these values. Suitable for advanced high school students studying statistics.

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