An engineer who is studying the tensile strength of a steel alloy intended for use in golf club shafts knows that tensile strength is approximately normally distributed withσ = 70 psi. A random sample of 12 specimens has a mean ten-sile strength of x = 3450 psi.

(a) Test the hypothesis that mean strength is 3500 psi. Use α = 0.05.

(b) What is the smallest level of significance at which you would be willing to reject the null hypothesis?

(c) What is the β-error for the test in part (a) if the true mean is 3470?

(d) Suppose that you wanted to reject the null hypothesis with probability at least 0.8 if mean strength μ = 3470. What sample size should be used?

(e) Explain how you could answer the question in part (a) with a two-sided confidence interval on mean tensile strength.

Suppose that Apex HealthServices has four difference projects.These projects are listed below, along with the amount of capital invested and estimated corporate and market betas: Project Amount Invested Corporate beta Market Betas walk-in-clinic 500,000 1.5 1.1 MRI facility 2,000,000 1.2 1.5 Clinical laboratory 1,500,000 0.9 0.8 X-ray laboratory 1,000,000 0.5 1.0 5,000,000 (a)why do the corporate and market betas differ for the same project? (b)what is the overall corporate beta of Apex HealthServices? Is the calculated beta consistent with corporate risk theroy? (c)what is the overall market beta of Apex Health services? (d) How does the riskiness of Apex's stock compare with the riskiness of an average stock? (e) would stock investors required rate of return on Apex that is greater than, less than,or the same as the return on an average-risk stock?

1a. Given: mean difference between men and women = 2.2; standard error of mean difference = 0.8; n men = 61, n women = 61.

Test the following null hypothesis at a=.05

Ho: u men = u women

Ha: u men > u women

You need to compute the t statistic, look up t critical value and make decision including likelihood of appropriate error. You don't have to compute the standard error of mean difference because it's given.

1b. Compute the appropriate confidence interval for the two-sample t-test of the previous question. Make sure you look at the alternative hypothesis before computing this interval.

Please upload into a Microsoft Word file and show work for answers

For 1b. please show work by doing step by step. line margins

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.8.

(a) Use the Normal approximation to find the probability that Jodi scores 74% or lower on a 100-question test. (Round your answer to four decimal places.)

(b) If the test contains 250 questions, what is the probability that Jodi will score 74% or lower? (Use the normal approximation. Round your answer to four decimal places.)

(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?

In a marine gas turbine unit a high-pressure turbine drives the compressor, and a low-pressure turbine drives the propeller through suitable gearing. The overall pressure ratio is 4/1, and the maximum temperature is 650⁰C. The isentropic efficiencies of the compressor, High Pressure turbine, and Low Pressure turbine are 0.8, 0.83 and 0.85 respectively, and the mechanical efficiency of both shafts is 98%.

Calculate the pressure entering the Low Pressure turbine when the air intake conditions are 1.01 bar and 25⁰C. Calculate also the thermal efficiency and the shaft power when the mass air flow is 60 kg/s. Neglect kinetic energy changes, and the pressure loss in combustion.

For all compression processes take c_p = 1.005 kJ/kg K and ɣ=1.4; for the combustion and expansion processes take c_p = 1.15 kJ/kg K and ɣ=1.333. Neglect the mass of fuel.

Consider two economies. In economy A:  autonomous consumption equals 700, the marginal propensity to consume equals 0.80, taxes are fixed at 50, investment is 100, government spending is 100, and net exports are 40.

In economy B: autonomous consumption equals 1000, the marginal propensity to consume equals 0.8, taxes are proportional to income such that consumers pay 25% of their income as taxes, investment is 250, government purchases are 150, and net exports are 400.

Question 1: What is the planned aggregate expenditure (PAE) in each economy?

Question 2:What is the short-run equilibrium output in each economy?

Question 3: In which economy is the spending multiplier higher?

Question 4:Suppose autonomous consumption fall by 500 in each economy. Which economy will see a higher drop in GDP? Compute the equilibrium output in each economy.

7. Consider the following income-expenditure model of a closed economy. The aggregate consumption function is C = 100 +0.8(Y – T); taxes are T = 380; investment, I, is 300 and government expenditure, G, is 200.

( a)Calculate the multiplier, equilibrium income and the government budget surplus [6 marks]

(b)Now let taxes, T = 10 + 0.25Y. Recalculate the multiplier, equilibrium income and the government budget surplus. Try to explain any differences between your answers and your answers to part (a). [10 marks]

( c)Now we further extend the model and open the economy to trade. Let net exports be NX = 444 - 0.3Y. Keep the tax function as in (b). Recalculate the multiplier and equilibrium income and again explain any differences between your answers and those in part (b). [10 marks]

A rectangular cross section beam (A) made of steel constructed in an industrial building
between two columns which are “X” m apart. The beam is acting as a support for one end of
a pair of crane wheel (B). The distance b/w wheels are “Y” m. The crane is used to lift max.
of Z tonnes of load which is having hook at the centre of crane. Draw shear force and B.M
diagram of the beam.
Case i) If the crane wheels are positioned at equal distances from centre of the beam.
Case ii) If one of the crane wheels is exactly at the centre.
Case iii) If one of the crane wheels comes exactly over a column.
Also find the max. bending stresses in the beam for the first case considering the depth (d)
as twice the width of the beam.
where X=4.8m,Y=0.8, Z =9 tonnes, Depth (d) = 500mm

Use the following information about the closed economy of Vanatu to answer questions 7 and 8:

Y=$35,000
T=$5,000 C=MPC*(Y-T)+$1000-1,000r MPC=0.8
G=$6,500
I=$4000-2,000r

8. Now suppose that the government of Vanatu wants to increase spending on military services. Assume that government purchases increase by $1,500. At the same time, assume the inflation rate in Vanatu is, and remains, 10%. Then

1. a) The nominal interest rate now is 76.7%; private savings increases

2. b) The nominal interest rate now is 67.5%; private savings decreases

3. c) The nominal interest rate now is 33.2%; private savings increases

4. d) The nominal interest rate now is 43.3%; private savings decreases

5. e) The nominal interest rate now is 57.7%; private savings increases

THE ANSWER IS A I AM JUST CONFUSED HOW TO GET THERE

A three-phase synchronous generator is rated 16 kV and 200 MVA, has negligible losses and has reactance of 1.65 pu. The generator is operated on an infinite bus of 15 kV voltage and delivers 100 MVA at 0.8 Power Factor, lagging.

a)Determine the internal voltage (E_i), the power angle (δ), and the line current of the machine.

b)If the field current of the machine is reduced by 10%, while the mechanical power input to the machine is maintained constant, determine the new value of the power angle (δ) and reactive power delivered to the system.

c)The prime mover is next adjusted without changing the excitation so that the machine delivers zero reactive power to the system. Determine the new power angle (δ) and the real power being delivered to the system.

d)What is the maximum reactive power that the machine can deliver if the level of excitation is maintained as in part b?