Hypotheses testing 1

A normal tomato will gain an average of 2 ounces per week during the growing season. A sample of 100 tomatoes is given a special hormone to increase their growth. The average weight gain of tomatoes in the sample was 3 ounces with a standard deviation of 1 ounce. Conduct a hypothesis test to determine if the hormone increased the tomatoes weight gain (Hint: (Embedded image moved to file: pic07419.jpg)). Assume Alpha = .01 and remember to clearly state your null and alternate hypothesis as well as your conclusion about the average weight gain of the tomatoes.

Differential Equation

Problem Details Mathematics, Ordinary Differential Equations Year 4 Solve numerically using the fourth order Runge-Kutta formulation Solve numerically using the fourth order Runge-Kutta formulation: dy/dx = -y-sin x Defined on the domain{ x : -pi < x , -pi } Given y (-pi) = 1.5. Use a step length h = pi/30 to help you in plotting on a graph for y over this domain. Include a table of coordinates Suggest a real world problem that may have a graph of this nature. Please ensure any attachments are in an easily accessible medium (eg. Word)

ODE (Runge-Kutta)

In the solution of the ODE : dy/dx = -y-sinx defined on the domain {x: -pi < x < pi} using 4th order Runge-Kutta I am trying to provide step-by-step detail of the first two steps (h=pi/30). Having seen these steps, I am confident I will be able to proceed with the problem.

What expected rate of return would a security earn if it had a 0.6 correlation with the market portfolio and a standard deviation of 3 percent

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 22 percent and a standard deviation of 5 percent. The risk-free rate is 4.9 percent, and the expected return on the market portfolio is 19 percent. Assume the capital-asset-pricing model holds. What expected rate of return would a security earn if it had a 0.6 correlation with the market portfolio and a standard deviation of 3 percent?

Based on the capital-asset-pricing model, what is the expected return on the above portfolio?

Suppose you have invested $50,000 in the following four stocks: Security Amount Invested Beta Stock A $10,000 0.7 Stock B 15,000 1.2 Stock C 12000 1.4 Stock D 13000 1.9 The risk-free rate is 5 percent and the expected return on the market portfolio is 18 percent. Based on the capital-asset-pricing model, what is the expected return on the above portfolio?