The one sample t statistic from a sample of n = 25 observations for the one-sided test of

H0: μ = 9, Ha: μ > 9

has the value t = 1.84. Based on this information, using Table C, the P-value should be
Question 8Select one:

a.
0.05 < P-value < 0.1.


b.
0.025 < P-value < 0.05.


c.
P-value > 0.10.


d.
P-value > 0.025.




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!

The one sample t statistic from a sample of n = 25 observations for the one-sided test of H0: μ = 9, Ha: μ > 9 has the value t = 1.84. Based on this information, using Table C, the P-value should be

Learn how to calculate the P-value for a one-sample t-test with a sample size of n = 25 and a test statistic t = 1.84. This problem covers key statistical concepts, including hypothesis testing, the t-distribution, and degrees of freedom. Suitable for undergraduate students studying introductory statistics.

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