A study was conducted to determine if the students from the public universities
take longer to graduate than the students from the private universities. 100
students from both the public universities and private universities were
surveyed. Suppose that from the years of research, it was known that the
population standard deviations were 1.58 years and 1 year respectively. The
following data were collected. The public and private universities students took
an average of 4.5 and 4.1 years respectively with a standard deviation of 0.3.
Use a 0.01 level of significance to test the claim.
(i) State the null and alternative hypotheses.

(ii) Is there any evidence to support the claim at α =0.01?

MANUAL CALCULATION

Let U be a Standard Uniform random variable. Show all the steps required to generate:

1. a Binomial random variable with parameters n = 12 and p = 0.6
2. a discrete random variable with the distribution P(x), where P(0) = 0.4, P(3) = 0.1, P(7) = 0.2, P(14) = 0.3;
3. a continuous random variable with the density f(x) = 4x 3 , 0 < x < 1;
4. a continuous random variable with the density f(x) = (1/18)x 2 , -3 < x < 3;
5. a continuous random variable with the density f(x) = (5/128)x 1/4 , 0 < x < 16

Suppose you are a policy maker who wants to select a level of saving rate that would maximize consumption per worker. Given that output per worker is a square root of capital per worker, and 10% of capital depreciates every year.
(a) Construct a table with the following saving rates: 0.3, 0.4, 0.5 and 0.6. For each saving rate, fill the table with values for capital per worker, output per worker, depreciation per worker, consumption per worker and marginal product of capital. Do not just present at able but show all your work clearly, or you lose marks.
(b) Which saving rate would you chose and why.

Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results:

R_HD =0.02+0.80R_M+e_HD

R-squared =0.6

                  R_ML =-0.03+1.50R_M+e_ML

R-squared =0.4

σ_M =0.20

where M is S&P/TSX Comp Index and R_X is the excess return of stock X.

1. What is the standard deviation of each stock? (Hint: b_i = (ρ_iM σ_i) / σ_M.)
2. What is the systematic risk of each stock?
3. What are the covariance and correlation coefficient between HD and ML?
4. For portfolio P with investment proportion of 0.3 in HD and 0.7 in ML, calculate the systematic risk, non-systematic risk and total risk of P.

**NO HANDWRITTEN ANSWERS PLEASE **

An automatic cookie machine at ACM, Inc. must deposit a specified amount of 25 0.3 grams (g) of dough for each cookie on a conveyor belt. It costs $0.03 to scrap a defective cookie. A sample of 50 cookies was drawn from the production process, which has been determined to be approximately normally distributed, and the results, in grams, can be found in worksheet tab Prob. 7-12 in the Excel file C07Data. a. What is the value of k in the Taguchi loss function? b. Determine how much the process varies from the target specification, based on the mean difference and standard deviation of the sample results. What is the expected loss per unit?

Q3)
A three-phase, Y-connected, 220 V, 13 kW, 60 Hz, six-pole induction motor has the following
parameter values in Ω/phase referred to the stator:
R1 = 0.3 Ω. R2' = 0.15 Ω
X1 = 0.5 Ω. X2'= 0.21 Ω Xm = 13.25 Ω
The total rotational losses are 450 W. The core loss is lumped in with the rotational losses. For a slip of 0.02,
and based on approximate equivalent circuit, determine:
(i) The rotor speed.
(ii) The stator current.
(iii) The power factor of the motor.
(iv) The input power of the motor.
(v) The developed mechanical power.
(vi) The efficiency of the motor.

You have a portfolio with a standard deviation of 30 % and an expected return of 18 %. You are considering adding one of the two stocks in the following table. If after adding the stock you will have 30 % of your money in the new stock and 70 % of your money in your existing​ portfolio, which one should you​ add?

Standard deviation of the portfolio with stock A is __%? (Round to two decimal places)

Standard deviation of the portfolio with stock B is __%? (Round to two decimal places)

Which stock would you add to your portfolio?

Given that Buffer A contains 200 ml of 0.05 M HOCl and 400 ml 0.03 M NaOCl, calculate the pH of the buffer solution, the pH of the solution after adding 10 mL of 0.5 M HCl, and the pH of the solution after adding 20 mL of 0.4 M NaOH.

Given that Buffer B contains 200 mL 0.5 HOCl and 400 mL 0.3 M NAOCl, calculate the pH of the buffer solution, the pH of the solution after adding 10 mL of 0.5 M HCl, and the pH of the solution after adding 20 mL of 0.4 M NaOH.

Which buffer will resist pH changes better?

QUESTION 5

If the flow hydrograph as listed in the Table Q5 passes through a stream reach from A to B, for which K = 8.0 hr and x = 0.3

1. Determine the peak outflow discharge at B. At t=0, the outflow discharge is 40 m³/s
2. Based on the inflow and outflow hydrograph, discuss the time lag required for the peak flood to reach the downstream area. Comment on the attenuation achieved.

Table Q5

In matlab ask the user to select whether to repeat the Newton-Raphson calculation or end the program. If the user exits out of the menu, repeat the request until the user makes a selection. If the program is repeated, store the new final value of the root and new number of iterations in the same variables without overwriting the previous results. Once the user chooses to end the program, save the variables containing the root values and numbers of iterations as calculation res.mat

this is my code so far

vector = input("Enter a vector which has an even number of elements: ");

the vector you enter is the polynomial you work with

the vector that is entered is [0.2 0.3 0 2.4 9.8 -21.4]