Question 1207902
**1. Calculate the Pooled Variance**

* Pooled variance (s_p^2) = ((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)
* s_p^2 = ((18 - 1) * 4.5 + (13 - 1) * 5.9) / (18 + 13 - 2) 
* s_p^2 = 5.06

**2. Calculate the Degrees of Freedom**

* Degrees of freedom (df) = n1 + n2 - 2 = 18 + 13 - 2 = 29

**3. Find the Critical Value**

* For a two-tailed test with α = 0.01 and df = 29, the critical values are:
    * t_critical = ±2.756 

**4. Calculate the Test Statistic**

* t = (x̄1 - x̄2) / √(s_p^2 * (1/n1 + 1/n2))
* t = (34.6 - 32.1) / √(5.06 * (1/18 + 1/13))
* t = 3.048

**5. Determine the P-value**

* Using a t-distribution table or statistical software, find the p-value associated with the calculated t-statistic (3.048) and degrees of freedom (29).
* The p-value will be less than 0.01.

**Therefore:**

* **(a) Rejection Region:**
    * t > 2.756
    * t < -2.756

* **(b) Test Statistic (t): 3.048**

* **(c) P-value: p-value < 0.010**