Question 1201153
**1. Set up Hypotheses**

* **Null Hypothesis (H0):** μ1 - μ2 = 0 (The average hourly wage charged by both agencies is the same.)
* **Alternative Hypothesis (Ha):** μ1 - μ2 ≠ 0 (The average hourly wage charged by both agencies is different.)

**2. Calculate the Pooled Variance**

* **Calculate the pooled variance (s²p):**
   * s²p = [(n1 - 1) * s1² + (n2 - 1) * s2²] / (n1 + n2 - 2)
   * s²p = [(20 - 1) * 1.45² + (18 - 1) * 1.25²] / (20 + 18 - 2)
   * s²p = [48.025 + 26.25] / 36
   * s²p = 2.064 

**3. Calculate the t-statistic**

* **t = (x̄1 - x̄2) / √[s²p * (1/n1 + 1/n2)]**
* t = (9.55 - 9.25) / √[2.064 * (1/20 + 1/18)]
* t = 0.3 / √[2.064 * (0.05 + 0.0556)]
* t = 0.3 / √[2.064 * 0.1056]
* t = 0.3 / √0.2179
* t = 0.3 / 0.4668
* t ≈ 0.642

**4. Determine Degrees of Freedom**

* Degrees of Freedom (df) = n1 + n2 - 2 = 20 + 18 - 2 = 36

**5. Find the Critical Value**

* Since this is a two-tailed test with α = 0.05 and df = 36, we find the critical values from the t-distribution table.
* The critical values are approximately ±2.028.

**6. Make a Decision**

* Since the calculated t-value (0.642) falls within the critical region (±2.028), we **fail to reject the null hypothesis.**

**Conclusion:**

At the 0.05 level of significance, there is **not enough evidence** to conclude that the average hourly wages charged by the two employment agencies are different. 

**Note:**

* This analysis assumes that the populations of hourly wages for both agencies are normally distributed.
* You can also use statistical software (like Excel or R) to perform the t-test and obtain the exact p-value.

I hope this helps! Let me know if you have any further questions.