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Do i reject at the significant levep 10%,5% and 1%

To determine whether to reject the null hypothesis at the given significance levels (10%, 5%, and 1%), we need to analyze the provided z-value and corresponding p-value.

Here’s the information from your data:
- **z-value**: 2.99024809
- **p-value**: 0.99860641

### Decision Rule:
- If the **p-value** is less than the significance level (\( \alpha \)), reject the null hypothesis (\( H_0 \)).
- If the **p-value** is greater than the significance level, fail to reject the null hypothesis.

### Comparison:
1. **At \( \alpha = 10\% (0.10) \):**
   - The p-value (0.99860641) is much greater than 0.10.
   - **Decision**: Fail to reject \( H_0 \).

2. **At \( \alpha = 5\% (0.05) \):**
   - The p-value (0.99860641) is much greater than 0.05.
   - **Decision**: Fail to reject \( H_0 \).

3. **At \( \alpha = 1\% (0.01) \):**
   - The p-value (0.99860641) is much greater than 0.01.
   - **Decision**: Fail to reject \( H_0 \).

### Conclusion:
At all three significance levels (10%, 5%, and 1%), the null hypothesis \( H_0: p < 0.7 \) cannot be rejected. This means there isn’t sufficient evidence to conclude that the proportion of students scoring more than 600 is greater than 70%.

Would you like a more detailed explanation of hypothesis testing or further breakdown? Let me know!  

### 5 Related Questions:
1. What is the importance of the z-value in hypothesis testing?
2. How do we interpret a very high p-value like 0.99860641?
3. What does a significance level represent in hypothesis testing?
4. How would the decision change if the p-value were lower than the significance level?
5. Can the sample size (90) impact the reliability of this hypothesis test?

### Tip:
When working with p-values, always ensure you clearly define your null and alternative hypotheses to avoid misinterpretation of the results.

Do I reject at the significant level 10%, 5%, and 1%?

Learn how to decide whether to reject a null hypothesis using z-scores and p-values at 10%, 5%, and 1% significance levels. This problem explores hypothesis testing, interpretation of p-values, and the rejection rule, based on a sample proportion greater than 600 from 90 observations.

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