a) The null: The proportion of registered voters who are planning to vote for the incument president <0.5 The alternative: The proportion of registered voters who are planning to vote for the incument president ≥0.5 b) Test statistic=(636/1200-0.5)/sqrt(0.5*0.5/1200)=2.08 c) CV is Z0.05=1.64 d) From the standard normal table, the p-value for the test statistic, z = 2.08 is 1-0.9812=0.0188. e) Since p-value is lower than 0.05, we reject the null and conclude that the proportion of registered voters who are planning to vote for the incument president increases significantly at 5% significance level. f) We say the proportion of registered voters who are planning to vote for the incument president increases significantly, while in fact it does not. g) We say the proportion of registered voters who are planning to vote for the incument president does not increases significantly, while in fact it does.
Part I – Thermodynamics Question 4 (10 marks) Consider an ideal Otto cycle, with a compression ratio of 11. At bottom dead centre before the compression, the air is at 100 kPa, 300 K. The temperature at the end of the isentropic expansion process is 700 K. Assume constant specific heats at room temperature, and the following properties of air: Cv = 0.718 kJ/kg.K, Cp = 1.005 kg/kg.K, R= 0.287 kJ/kg.K and γ = 1.4. (a) Show and label the cycle on a P-v diagram, labelling all states, work and heat transfer processes. (4 marks) (b) Find the temperature and pressure at the beginning of the constant volume heat addition process. (2 marks) (c) Find the temperature and pressure at the beginning of the isentropic expansion process. (2 marks) (d) Determine the efficiency of the cycle. (2 marks)
Part II – Fluid Mechanics Question 3：
A cylindrical vessel is partially filled with water, and starting from rest the vessel is rotated at a constant angular velocity 𝜔. The velocity 𝑉 within the fluid depends on radial location 𝑟, the time from the start of rotation 𝜏, 𝜔 and the fluid properties. (i) Find the non-dimensional groups that relate 𝑉 and the other parameters of relevance. (8 marks) (ii) If, in another experiment, honey is rotated in the same vessel at the same angular speed, determine from your dimensionless parameters the ratio of the time for the honey and water to attain the steady motion. Assume water and honey to be of the same density and honey to be 2000 times more viscous than water. (4 marks) (iii) At steady state, determine and explain briefly which non-dimensional groups will be irrelevant. Then, from the remaining relevant group/s determine how 𝑉 will vary with 𝑟. (4 marks)