To determine the P-value for the one-sample t-test, we can follow these steps:

1. We know that the test statistic is $t = 1.84$.
2. The degrees of freedom (df) for a t-test is calculated as $df = n - 1$, where $n = 25$. So, $df = 25 - 1 = 24$.
3. Since it's a one-sided test with the alternative hypothesis $H_a: \mu > 9$, we want the area to the right of $t = 1.84$.

Using Table C (which is typically a t-distribution table):

We look up the critical values for $t$ with 24 degrees of freedom.

• The closest values for $t = 1.84$ are between 1.711 (which corresponds to a right-tail probability of 0.05) and 2.064 (which corresponds to a right-tail probability of 0.025).

Thus, the P-value lies between 0.05 and 0.025.

Conclusion:

The correct answer is:

b. 0.025 < P-value < 0.05.

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Do you want more details or have any questions on this?

Here are 5 related questions for further exploration:

1. What are the degrees of freedom in a t-test, and how are they calculated?
2. How does a one-sided test differ from a two-sided test?
3. What is the relationship between the t-statistic and the P-value?
4. How do you interpret a P-value in the context of hypothesis testing?
5. What happens if the P-value is smaller than the significance level?

Tip: Always double-check the degrees of freedom and the alternative hypothesis to ensure correct interpretation of the t-distribution table!