Question 1199985
**1. Set up Hypotheses**

* **Null Hypothesis (H0):** 
    * μ₁ - μ₂ ≤ 0 
    * The mean annual rate of return for NYSE stocks is less than or equal to the mean annual rate of return for NASDAQ stocks.

* **Alternative Hypothesis (H1):** 
    * μ₁ - μ₂ > 0 
    * The mean annual rate of return for NYSE stocks is greater than the mean annual rate of return for NASDAQ stocks.

**2. Calculate Sample Statistics**

* **NYSE:**
    * Sample size (n1) = 11
    * Sample mean (x̄₁): 16.77
    * Sample standard deviation (s1): 5.29

* **NASDAQ:**
    * Sample size (n2) = 12
    * Sample mean (x̄₂) = 14.59
    * Sample standard deviation (s2): 5.96

**3. Calculate Pooled Standard Deviation**

* Pooled standard deviation (sp) = √[((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)]
* sp = √[((11 - 1) * 5.29^2 + (12 - 1) * 5.96^2) / (11 + 12 - 2)]
* sp ≈ 5.64

**4. Calculate t-Statistic**

* t = (x̄₁ - x̄₂) / [sp * √(1/n1 + 1/n2)]
* t = (16.77 - 14.59) / [5.64 * √(1/11 + 1/12)]
* t ≈ 0.67

**5. Determine Degrees of Freedom**

* Degrees of freedom (df) = n1 + n2 - 2 = 11 + 12 - 2 = 21

**6. Find the Critical Value**

* Since this is a one-tailed test with α = 0.10 and df = 21, the critical value from the t-distribution table is approximately 1.323.

**7. Compare t-Statistic to Critical Value**

* Calculated t-statistic (0.67) is less than the critical value (1.323).

**8. Make a Decision**

* Since the t-statistic does not fall in the rejection region, we **fail to reject the null hypothesis**.

**9. Conclusion**

* At the 0.10 significance level, there is **not enough evidence** to conclude that the mean annual rate of return for stocks listed on the NYSE is higher than the mean annual rate of return for stocks listed on NASDAQ.