(b) A sample of ten diabetic women is selected; their mean diastolic blood pressureis =84 mm Hg. Using this information, conduct a two-sided test at the =0.05level of significance. What is the p-value of the test? (5 %)

題組內容

1. The distribution of diastolic blood pressures for the population of female diabeticsbetween the ages of 30 and 34 has an unknown mean and standard deviation =9.1mm Hg. It may be useful to physicians to know whether the mean of thispopulation is equal to the mean diastolic blood pressure of the general populationof females in this age group, 74.4 mm Hg.

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%)

題組內容

(b) A sample of ten diabetic women is selected; their mean diastolic blood pressureis =84 mm Hg. Using this information, conduct a two-sided test at the =0.05level of significance. What is the p-value of the test? (5 %)

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