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

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.

**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

An investor purchased 550 shares of stock A at $22.50 per share and 1,050 shares of stock B at $30.50 per share one year ago. Stock A and stock B paid quarterly dividends of $2.50 per share and $2.00 per share, respectively, during the year. One year later, the investor sold both stocks at $30.50 per share. The correlation coefficient (ρ_AB) is 0.3 and the standard deviations of stock A and stock B are 20.5 percent and 15.5 percent, respectively.

Calculate the standard deviation of the portfolio. (Round intermediate calculations to 4 decimal places, e.g. 15.2512 and the final answer to 2 decimal places, e.g. 15.25%.)

1. A stock portfolio has an expected return of 12% and a standard deviation of 20%. A bond portfolio has an expected return of 6% and a standard deviation of 9%. The two portfolios have a correlation coefficient of 0.3. T-Bills have an expected return of 2%. Your coefficient of risk aversion is 7. (15 points)

1. What are the weights of the minimum variance portfolio that can be formed between the two portfolios if they are the only risky assets being considered?

2. What is the expected return and standard deviation of the minimum variance portfolio?

3. How much should you allocate between T-Bills and the risky portfolio?

4. What is the expected return and standard deviation of your complete portfolio?

use r programming, details on the codes please.

Consider an urn with 10 balls inside, 7 of which are red and 3 of which are green. Select 3 balls successively from the urn. Let A = {1 st ball is red}, B = {2 nd ball is red}, and C = {3 rd ball is red}. Then P(all 3 balls are red) = P(A ∩ B ∩ C)

     a) Calculate the Probability with R? (1)

     b) Also, what is the probability of observing red, then green, then red? (1)

Let us roll a 4-sided die three times. a)Let us define the random variable U = X1 − X2 + X3. What is the probability that U > 6. (1) b) Also, if A = X1+X2+X3, What is the probability of A > 9.(1)

3. Randomized Controlled Trials are a type of medical experiment, where the eligible participants are randomly assigned (allocated) to one of the two (or more) branches of the study. A randomized controlled trial is considered the gold standard of clinical trials. In these studies, randomization helps to control for confounding factors, and evenly distribute prognostic factors across groups. This is somewhat like a loaded dice experiment.

            Let’s create an “unfair” dice that has a 0.35 probability of resulting in a 6, and a    probability of 0.13 for each of the other outcome.

Hint: Use the sample command.

a) Simulate a sample of 10 trials of throwing the dice. (1)

b) How many 6’s do you get count using R. (1)

Write a function cancerservival where the probability of cure, recurrence, metastasis and death are (0.3, 0.3, 0.25 and 0.15 respectively). (2)
a) Use the function to simulate the results of 100 cancer occurrences. (1)

b) Report the number of patients cured. (1)