 The data supports the claim that the average diameter of ball bearing from this manufacturing process is greater than 2.30.  I could also confirm this from observing the confidence intervals that the chances of the population mean to lie somewhere greater than 2.30 is high. 

Since the p-value (0.03895) is too large or greater than 0.01 that concludes the results are not significant which means it you don't reject the null hypothesis.   is this right?

Your statement contains some correct points, but there's a misunderstanding about the interpretation of the p-value. Let’s break this down clearly:

1. **Claim about the average diameter**: You mention that the average diameter is greater than 2.30, and that the confidence intervals suggest the population mean is likely greater than 2.30. This is consistent with the idea that the confidence interval provides evidence supporting the alternative hypothesis (mean > 2.30).

2. **Interpretation of the p-value (0.03895)**:
   - A **p-value** is used to determine whether to reject the null hypothesis.
   - **Null Hypothesis (H₀)**: The population mean is ≤ 2.30.
   - **Alternative Hypothesis (H₁)**: The population mean is > 2.30.
   - The p-value of **0.03895** indicates the probability of observing your data (or something more extreme) under the assumption that the null hypothesis is true.

3. **Significance Level**: 
   - A p-value of 0.03895 is **smaller** than the typical threshold of 0.05 (5% significance level), which means the result is significant at this level, and you **reject** the null hypothesis at a 5% significance level.
   - However, since you are comparing it to 0.01, it is **greater** than 0.01, meaning the result is **not significant** at a 1% significance level.

4. **Conclusion**:
   - Since the p-value (0.03895) is **less than 0.05**, you **reject the null hypothesis** at the 5% level, and conclude that the mean diameter is greater than 2.30.
   - But because the p-value is **greater than 0.01**, the result is **not significant** at the 1% level. Therefore, you do not reject the null hypothesis if your threshold is 1%.

### To summarize:
- If your significance level is 5%, the result **is significant** and you **reject the null hypothesis**.
- If your significance level is 1%, the result **is not significant** and you **do not reject the null hypothesis**.

---

Would you like more details on how to choose the right significance level or other aspects of hypothesis testing?

### Relative Questions:
1. How do you determine the best significance level for hypothesis testing?
2. Can the confidence interval be used to directly reject or accept a null hypothesis?
3. What are the risks of using a 1% significance level compared to a 5% one?
4. How would a larger sample size affect the p-value and confidence intervals?
5. How does statistical power relate to p-values and significance levels?

**Tip**: Always predefine your significance level (α) before conducting a test to avoid bias in interpreting p-values.

The data supports the claim that the average diameter of ball bearing from this manufacturing process is greater than 2.30. I could also confirm this from observing the confidence intervals that the chances of the population mean to lie somewhere greater than 2.30 is high. Since the p-value (0.03895) is too large or greater than 0.01 that concludes the results are not significant which means it you don't reject the null hypothesis. Is this right?

Understand how to interpret p-values and confidence intervals in hypothesis testing. This example evaluates whether the average diameter of ball bearings is greater than 2.30 and explains the significance levels of p-values 0.03895 and 0.01. Suitable for high school and college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation