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.