3. 一新醫學療法宣稱，其在延長癌症末期病人的壽命方面，較傳統療法更具效果。根據醫學期刊紀錄，在傳統療法下，病人平均延長 4.2 年的壽命，而根據對 80 位病人接受新療法所得到的結果，其樣本平均值與標準差分別為 4.5 年和 1.1 年。在顯著水準=0.05 下，檢定這個宣稱是否正確？(10 %)

3. Migration is a central issue for the 2024 US presidential election, with debates focusing on its economic, social, and political impacts. Suppose that there are two countries, Country 1 and Country 2, each with two types of labor: high-skilled (H) and low-skilled (L). Both countries have the same amount of physical capital, high-skilled labor and low-skilled labor but differ in how labor inputs contribute to production. The production functions for the two countries are:$Y_1 = A K_1^\alpha L_1^\beta H_1^{1-\alpha-\beta},$$Y_2 = A K_2^\alpha (L_2 + \eta H_2)^{1-\alpha}.$where $K_1$ and $K_2$ are physical capital in Country 1 and Country 2, $\eta > 1$ is the relative productivity of high-skilled labor to low-skilled labor in Country 2, and $0 < \alpha < 1$, $0 < \beta < 1$. Assume all markets are competitive. Answer the following questions.(a) Derive the marginal product of high-skill and low-skill labor, express the high-to-low skilled wage ratio in terms of the parameters, and discuss whether high-skilled labor and low-skilled labor are complements or substitutes in production for both Country 1 and Country 2. (10%)

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