Girls of a certain age in the nation have a mean weight of 85 with a standard deviation of 10.8 lb. A complaint is made that girls are underfed fed in a municipal children's home. As evidence, a sample of 25 girls of the given age is taken from the children's home with a mean weight of 89.41 lb. What can be concluded with α = 0.01?

a) What is the appropriate test statistic? (choose one of the following)

1. na 2. z-test 3. one-sample test 4. independent-samples t-test 5. related-samples t-test

b1)
Population: (choose one of the following)

1. weight 2. children's home 3. girls in the nation 4. feeding method 5. girls from the children's home

b2)
Sample: (choose one of the following)

1. weight 2. children's home 3. girls in the nation 4. feeding method 5. girls from the children's home

c) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value = __________; test statistic = _________

Decision:

1. Reject H0 or 2. Fail to reject H0?

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[ ], [ ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d = ___________ ;   *(choose one)1. na 2. trivial effect 3. small effect 4. medium effect 5. large effect
r² = ___________ ;   *(choose one)1. na 2. trivial effect 3. small effect 4. medium effect 5. large effect

f) Make an interpretation based on the results. (choose one)

a. The weight of girls in the children's home was significantly higher than the weight of girls in the nation.

b. The weight of girls in the children's home was significantly lower than the weight of girls in the nation.  

c. The weight of girls in the children's home was not significantly different than the weight of girls in the nation.

Reese’s pieces are supposed to be 50% orange, 25% yellow, and 25% brown. Suppose your random sample is of size 500. Let ?̂be the proportion of orange piece in your sample.

2. Which parameter is being estimated by ?̂?

A. The true average number of orange piece in your sample.

B. The true average number of orange piece in all Reese’s pieces.

C. The true proportion of orange piece in your sample.

D. The true proportion of orange piece in all Reese’s pieces.

3. The mean of ?̂is ____.

4. The standard deviation (sometimes called standard error) of ?̂is ____. (4 decimal places)

5. Which of the following can best describe/explain the shape of ?̂?

A. We can’t determine the shape of ?̂.

B. ?̂follows normal distribution because: 1. The sample is random. 2. ? is large enough, i.e. ? = 50% = 0.5 ≥ 0.5

C. ?̂follows normal distribution because: 1. The sample is random. 2. ? = 500 ≥ 30.

D. ?̂follows normal distribution because: 1. The sample is random. 2. ?? = 500(0.5) = 250 ≥ 5 and ?(1 − ?) = 500(0.5) = 250 ≥ 5

6. What is the probability that you have less than 230 orange pieces in your sample? (4 decimal places)

UNIT 1 Classify the following as microeconomics or macroeconomics and provide a justification for your choice. (i) The effect of changes in household saving rates on the growth rate of national income. (ii) The effect of rising oil prices on employment in the airline industry. (iii) A comparison of alternative tax policies and their respective impacts on the rate of the nation’s economic growth. (iv)Changes in the nation’s unemployment rate over short periods of time. UNIT 2 (a) Your marginal benefit from eating hotdogs is shown in the table below: # Hotdogs Marginal Benefit (MB) 0 0 1 7 2 4 3 2 4 1 If the price of a hotdog is $3 how many should you buy? Provide a justification for your choice. (b) The number of toys produced per day are shown in the table below: Workers Toys produced 1 48 2 88 3 112 4 168 5 176 6 192 7 224 8 216 9 224 10 208 (i) What is the marginal product of the 5th worker? the 9th worker? (ii) What is the maximum number of toys that should be produced? What is the maximum number of workers that should be hired? Explain.

*Please give the answers in pseudo code

1) Design an algorithm that will receive two integer items from a terminal operator, and display to the screen their sum, difference, product and quotient. Note that the quotient calculation (first integer divided by second integer) is only to be performed if the second integer does not equal zero.

2) Design an algorithm that will read two numbers and an integer code from the screen. The value of the integer code should be 1, 2, 3 or 4. If the value of the code is 1, compute the sum of the two numbers. If the code is 2, compute the difference (first minus second). If the code is 3, compute the product of the two numbers. If the code is 4, and the second number is not zero, compute the quotient (first divided by second). If the code is not equal to 1, 2, 3 or 4, display an error message. The program is then to display the two numbers, the integer code and the computed result to the screen.

3) Design an algorithm that will receive the weight of a parcel and determine the delivery charge for that parcel. Charges are calculated as follows:
Parcel weight (kg)
Cost per kg ($)
<2.5
$3.50 per kg
2.5-5 kg
$2.85 per kg
>5 kg
$2.45 per kg

Problem 2: Valuation on a Multiplicative Binomial Lattice

This problem reviews some of the main ideas of valuation on a binomial lattice and the properties of put and call options. You may wish to review the relevant lecture material and readings.

Suppose that the price of a share of KAF stock is S(0) = £120 in period 0. At the beginning of period 1, the price of a share can either move upward to S(1) = u S(0) or downward to S(1) = d S(0). Suppose that u = 4/3 = 1.333 and d = 3/4 = .75, so that S(1) = u S(0) = £160 after an up move and S(1) = d S(0) = £90 after a down move. Suppose that the probability of an up move is p = 0.5.

Similarly, suppose that, at the beginning of period 2, the share price either moves up or down by the same multiplicative factors and with the same probability (0.5) of an up move. (If the probability of an up move in a period is 0.5, then the probability of a down move in a period is also 0.5.) Hence, if the share price in period 1 is S(1), then the share price at the beginning of period 2 is either S(2) = u S(1) = 4/3 S(1) or S(2) = d S(1) = 3/4 S(1).

For simplicity, suppose that a period is a year, and let the riskless interest rate be r = .12, that is, 12% per period.

2. (i) Briefly explain what is meant by an Arrow-Debreu 1-period-ahead down security and the 1-period-ahead down state price.

(ii) Write down two equations that describe a replicating portfolio of KAF shares and riskless bonds that has a payoff of 1 in period 1 if the price of a KAF share moves downward at the beginning of period 1 and has a payoff of 0 otherwise. Briefly explain your reasoning.

Calculate the number of shares of KAF stock and the amount of riskless bonds in the replicating portfolio.

(Recall that buying riskless bonds is equivalent to lending money at the riskless rate of interest and selling riskless bonds short is equivalent to borrowing money at the riskless rate. A negative number of shares in a portfolio corresponds to selling those shares short.)

You are deciding between two mutually exclusive investment opportunities.

Project A requires an investment of $1,000 at t = 0 and generates a perpetual cash flow of $150 starting at t = 1.

Project B requires an investment of $1,000 at t = 0 and generates a cash flow of $60 at t = 1. After t = 1 the cash flow grows at the rate of 4% in perpetuity (so the cash flow at t = 2 is 4% higher than the cash flow at t = 1, the cash flow at t = 3 is 4% higher than the cash flow at t = 2 and so on).

a. Which investment has the higher IRR?

b. Which investment has the higher NPV when the cost of capital is 6%?

c. Which investment should you pick (if any) if the cost of capital is 6%? d. For what range of values for the opportunity cost of capital would you make the opposite decision, compared to part c?

a.) In families of 4 offspring, what is the probability of finding the oldest and youngest offspring to both be female?

(As you calculate your response, keep variable rounded at 4 decimal places, provide your answer as a percentage with 2 decimal places, no percentage sign needed(%) i.e., 45.21)

b.) Chestnut, Palomino, and Cremello coat coloring is horses is determined by a partial or incomplete dominant mode of inheritance. Chestnut (CC) and cremello (C^CrC^Cr)

animals have a homozygous genotype, and palomino coat coloring is a result from a heterozygous genotype (CC^Cr)

Two palomino horses have created 3 offspring. What is the chance that these 3 offspring result in 1 of each color (1 chestnut, 1 cremello, and 1 palomino) colts?

(As you calculate your response, keep variable rounded at 4 decimal places, provide your answer as a percentage with 2 decimal places, no percentage sign needed(%)i.e., 45.21)

A researcher measured the number of hours of community service performed during an average week in a sample for three adolescent and young adult age groups. The results are shown below.  

14 year olds                17 year olds                21 year olds

            5                                              8                                              3         

         6                                                12                                            5

          3                                                7                                              7

            5                                              4                                              4                

Conduct a one-way ANOVA to determine if there are any differences between the groups on community service. The test is 2 –tailed, with an alpha of .05, and the critical F is 4.26. Make sure answers are clearly labeled and well-organized.

Step 1 (1 pts) Restate the question as an alternative hypothesis and a null hypothesis about the populations

Step 2 (1 pts) Determine the characteristics of the comparison distribution.

Step 3 (1 pt) Find the threshold (critical) value on the comparison distribution

Step 4 (3 pts) Determine your sample’s score on the comparison distribution.

Project Monitoring and Control Process Plan:
You have a Project Budget for building a five-bedroom house in Ashburn, VA. Assume that your building project is two months behind and has a $100,000.00 cost overrun. This should not be a surprise to you because of the monitoring processes. Identify and discuss some of the monitoring processes that could have alerted you of the schedule and cost problems. What are some of the controlling steps you would take to bring both the schedule and the cost back on track? Be sure to justify your answers. . Your Project Monitoring and Control Process Plan should be at least two pages including a summarization and conclusion page. If necessary, include data from the Project Budget and Project Schedule in the table shown below to support your schedule and cost problems.