1. Researchers doing a study of incomes in a large metropolitan area want to determine if residents in Suburban District 1 have different mean income from residents in Suburban District 2. They collected the data and found the following sample means and variances. Use these data to conduct a hypothesis test of their research question, using α = .05.

1. State the null and alternative hypotheses in words and in symbols. (4 points)

2. Is this a one-sided or a two-sided test? How do you know? (3 points)

3. Should you use a z-test or a t-test for this problem? Why? (3 points)

4. Find the critical value of the test statistic. (4 points)

5. Calculate the value of the test statistic for this sample. (8 points)

6. Based on these results, can you reject the null hypothesis or not? Write a sentence to explain your conclusion. (4 points)

(1) Suppose a company just paid a dividend of $3.6. Its manager promises to pay annual dividend growing at 6% per year. If the required return is 12% (in EAR), what would the current price be?

(2) Now assume the manager has decided to pay quarterly dividends instead of annual dividends. It has just paid a dividend of $0.9. The next dividend will be 3 months from now, with value equal to $0.9*(1.06)^1/4, and will grow at an annual rate of 6%. That is, each dividend payment will be 1.06^(1/4) times the previous one. What is the share price now?

(3) Now assume the dividend will grow more slowly at a rate of 2% per year from the 40th quarterly dividend. That is, the 41st dividend will be equal to the 40th dividend multiplied by (1.02)^1/4. What is the share price now?

Please answer the question using formulas, do not use excel or other techniques that are not allowed to use during a standardized test.

1. This same researcher collected at random one child from each of the eight families in which there was at least one child. She recorded the following data to study the effects of number of siblings (X) on happiness of the child (Y), measured on an interval scale in which low scores indicate a low level of happiness and high scores indicate a high level of happiness:

                 X                   Y    

                 1                   5

                 0                   3

                 2                   4

                 4                   7

                 2                   5

                 3                   9

                 1                   8

                 1                   4    

1. Draw a scatter plot of the data.
2. Write out the regression equation, then calculate and interpret the meaning of the regression slope and Y-intercept. See problem 1 for an explanation of the guidelines for interpretation.
3. Draw the regression line on the scatter plot.
4. Predict the happiness of an only child and the happiness of a child with two siblings.
5. Find the coefficients of determination and non-determination and interpret what they mean.
6. Is the relationship between happiness level and number of siblings statistically significant using a 95% confidence level?

Write Java code for each of the following problem

a. Two players, a and b, try to guess the cost of an item. Whoever gets closest to the price without going over is the winner. Return the value of the best bid. If both players guessed too high, return -1.
example:
closestGuess(97, 91, 100) → 97
closestGuess(3, 51, 50) → 3
closestGuess(12, 11, 10) → -1

b. Given a non-empty string, return true if at least half of the characters in the string are the lowercase letter z.
example:
zMajority("az") → true
zMajority("zabzc") → false
zMajority("w") → false

c. Given 4 numbers, return the value of the second largest number. Note that if two or more numbers are tied for largest, then the second largest value is also the largest value.
example:
secondLargest(1, 2, 3, 4) → 3
secondLargest(3, 2, 1, 4) → 3
secondLargest(5, 7, 5, 9) → 7

Superposition of N harmonic oscillator waves of equal amplitude equal angular frequency ω and constant incremental phase difference φ. And constant spacing d between them. The total length of the array of the oscillator is L. With L = N*d

The amplitude is: where A0 the amplitude of each wave. A = A0 sin(Nφ /2) / sin(φ /2)

The intensity : I = I0*(sin(Nφ /2) / sin(φ /2))^2

1. show the minimum is at Nd*sin(θ ) = m λ, m =?

2. The principal maximum is at d*sin(θ ) = m λ 3. Secondary maximum is at Nd* sin(θ ) = (m+1/2) λ, m=? 4. Let β = Nφ , show that as N-> infinite and φ → 0 The intensity → I = 4 Im * ( sin(β/2) / β )^2 Where Im = N^2 * I0

5. show that minimum is at a*sin(θ ) = m λ and maximum is at a*sin(θ ) = (m+1/2) λ (Intensity drops drastically) Where a is the width of a single slit

6. Show that if I: intensity inversely square decreases of r, distance from the source, then the amplitude inversely decreases of r.

1. For each of the following production functions (a-c) answer the following questions (i-v):

i) Calculate the marginal products MPL and MPK.

ii) Calculate MRTSL;K and determine if this is diminishing as good L increases.

iii) If Q0 = 100, w = 8 and r = 2, determine long-run cost minimizing combination of labor and capital and the associated total cost.

iv) If Q0 = 100, w = 8 and r = 2, determine short-run cost minimizing combination of labor and capital and the associated total cost if the firm is stuck with K = 4 unit of capital in the short run.

v) Do we have too much or too little capital in the short run, and how much money is the firm losing by being stuck with K = 4 unit of capital in the short run?

(a) Q(L;K) = 10L^1/2K^1/2.

(b) Q(L;K) = 4L^2 + 4K^2.

(c) Q(L;K) = 4LK + 6K.

Suppose two countries have labor inputs as represented in the table below. Based on the information in this table, country B has

a.    absolute advantage in the production of both goods.

b.    comparative advantage in the production of both goods.

c.    absolute disadvantage in the production of S.

d.    comparative advantage in the production of S.

4. According to the table, country A has comparative advantage in the production of

a.    good S.

b.    good T.

c.    both goods.

d.    neither good.

5. In this example, the equilibrium terms of trade (P_S/P_T) could occur anywhere

a.    between 3/4 and 5/4

b.    between 3/4 and 4/3

c.    between 1/3 and 4/3

d.    between 1/2 and 3/4

PYTHON

1- First, initialize the constant NUMS as 3: NUMS=3
2- Print the title of the application.
>---=== Python Temperature Analyzer ===---<
3- Using a for loop, prompt the user to enter the high and low values for each of NUMS days. The values entered must be between -40 and 40, and high must be greater than low.
Print the following messages:
>
* Read the high value.
>
Enter the high value for day 1:
< (or day 2, or day 3)
Enter the low value for day 1:
< (or day 2, or day 3)

* Read the low value.
IMPORTANT: You may only declare two (2) int type variables for the high and low values
4- Useanestedwhile(ordo-while)looptoanalyzetheresults,highmustbegreaterthan low, high must be less than 41, low must be greater than -41
*If any entry is incorrect, prompt the user to enter again until the entries pass the tests:
>
<
Then prompt again for the high and low temperatures for the day.
OUTPUT EXAMPLE (Red numbers show the input)
--== Python Temperature Analyzer ==-- Enter the high value for day 1: 8
Enter the low value for day 1: -2
Enter the high value for day 2: 41
Enter the low value for day 2: -4
Incorrect values, temperatures must be in the range -40 to 40, high must be greater than low.
Enter the high value for day 2: 9
Enter the low value for day 2: -4
Enter the high value for day 3: 5
Enter the low value for day 3: 11
Incorrect values, temperatures must be in the range -40 to 40, high must be greater than low.
Enter the high value for day 3: 11 Enter the low value for day 3: 5

* Read the high value.

>

0. 1- First, initialize the constant NUMS as 3: NUMS=3

   2- Print the title of the application.

   >---=== Python Temperature Analyzer ===---<.

1. 3- Using a for loop, prompt the user to enter the high and low values for each of NUMS days. The values entered must be between -40 and 40, and high must be greater than low.

   Print the following messages:

   >

* Read the low value.
IMPORTANT: You may only declare two (2) int type variables for the high and low values

4- Useanestedwhile(ordo-while)looptoanalyzetheresults,highmustbegreaterthan low, high must be less than 41, low must be greater than -41

*If any entry is incorrect, prompt the user to enter again until the entries pass the tests:

>
<

Then prompt again for the high and low temperatures for the day.

OUTPUT EXAMPLE (Red numbers show the input)

--== Python Temperature Analyzer ==-- Enter the high value for day 1: 8

Enter the low value for day 1: -2

Enter the high value for day 2: 41

Enter the low value for day 2: -4

Incorrect values, temperatures must be in the range -40 to 40, high must be greater than low.

Enter the high value for day 2: 9

Enter the low value for day 2: -4

Enter the high value for day 3: 5

Enter the low value for day 3: 11

Incorrect values, temperatures must be in the range -40 to 40, high must be greater than low.

Enter the high value for day 3: 11 Enter the low value for day 3: 5

>

* Read the high value.

>

0. 1- First, initialize the constant NUMS as 3: NUMS=3

   2- Print the title of the application.

   >---=== Python Temperature Analyzer ===---<

3- Using a for loop, prompt the user to enter the high and low values for each of NUMS days. The values entered must be between -40 and 40, and high must be greater than low.

Print the following messages:

* Read the low value.
IMPORTANT: You may only declare two (2) int type variables for the high and low values

4- Useanestedwhile(ordo-while)looptoanalyzetheresults,highmustbegreaterthan low, high must be less than 41, low must be greater than -41

*If any entry is incorrect, prompt the user to enter again until the entries pass the tests:

>
<

Then prompt again for the high and low temperatures for the day.

OUTPUT EXAMPLE (Red numbers show the input)

--== Python Temperature Analyzer ==-- Enter the high value for day 1: 8

Enter the low value for day 1: -2

Enter the high value for day 2: 41

Enter the low value for day 2: -4

Incorrect values, temperatures must be in the range -40 to 40, high must be greater than low.

Enter the high value for day 2: 9

Enter the low value for day 2: -4

Enter the high value for day 3: 5

Enter the low value for day 3: 11

Incorrect values, temperatures must be in the range -40 to 40, high must be greater than low.

Enter the high value for day 3: 11 Enter the low value for day 3: 5