SOLUTION: Hello, please i need help solving this: The Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the averag

Question 1201153: Hello, please i need help solving this: The Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the average hourly wage charged by both agencies is the same. A Donaldson manager surveyed other employers in town to find what they paid the agencies for temporary secretaries. The results are summarized below. At alpha = 0.05, test the claim that each agency charges the same hourly wage.
Agency A: x1 = 9.55/hr, $1 =$1.45/hr, n1= 20.
Agency B: x1 = 9.25/hr, $1 =$1.25/hr, n1= 18.

Answer by GingerAle(43) (Show Source): You can put this solution on YOUR website!
**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.

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