The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 76.3 with a standard deviation of 5.6. A random sample of 17 supermarkets from Region 2 had a mean sales of 86.5 with a standard deviation of 6.8. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.1 for the test. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 4 : State the null and alternative hypotheses for the test. Step 2 of 4 : find the value test statistic Step 3 of 4 : determine the decision rule for the null hypothesis. round to 3 decimal places. Step 4 of 4 : state the tests conclusion

Over a 4 year period the black corp purchased 100% of the outstanding voting shares of White Co. The acquisition was made in a series of steps as follows:

DATE:                             %                        Purchase Price

Jan 1, Year 1 5% 5,000

Jan 1, Year 2 10% 12,000

Jan 1, Year 3 10% 15,000

Jan 1, Year 4 75% 200,000

Total 100% 232,000

Any excess of the purchase price over the net book value of the assets was attributed to goodwill.

The acquisition in Year 3 allowed Black to have significant influence over the operating policies of white.

The acquisition in Year 4 gave Black control over White.

Operating results, dividends paid and fair value of white for the 4 years were as follows:

Net Income Dividend Paid Fair Value

Jan 1 Year 1 100,000

Year 1 25,000 15,000 120,000

Year 2 30,000 15,000 150,000

Year 3 40,000 20,000 170,000

Year 4 50,000 25,000 250,000

1. For each of the 4 years compute the amount of income that will be recorded on Black’s books related to its investment in White Co. AND compute the balance in “Investment in White Co. Account” on Blacks books at December, 31 of each year

*SHOW ALL WORK*

State the hypotheses to be tested

Run the appropriate regression test

Write the regression model equation

What is the strength of the relationship?

Using the equation, predict the price of a Coop Apartment with 2640 sq feet, 2 bedrooms and is 2 years old.

Interpret b3 in your equation from part c

1. (14) List the elements for each of the following sets:

(1) P({a, b, c})                                                         (Note: P refers to power set)

(2)   P{a, b}) - P({a, c})

(3)   P(Æ)

(4) {x Î ℕ: (x £ 7 Ù x ³ 7}                        (Note: ℕ is the set of nonnegative integers)

(5)   {x Î ℕ: $y Î ℕ (y < 10 Ù (y + 2 = x))}           

(6)    {x Î ℕ: $y Î ℕ ($z Î ℕ ((x = y + z) Ù (y < 5) Ù (z < 4)))}

(7)   {a, b, c} x {c, d}                                                 (Note: x refers to Cartesian product)

2. (12) True or False.

Let R = {(1, 2), (2, 3), (1, 1), (2, 2), (3, 3), (1, 3)}.

(1) R is reflexive.

(2) R is transitive.

(3) R is symmetric.

(4) R is antisymmetric.

3. (16) True or False.

(1) Subset-of is a partial order defined on the set of all sets.

(2) Subset-of is a total order defined on the set of all sets.

(3) Proper-subset-of is a partial order defined on the set of all sets.

(4) Proper-subset-of is a total order defined on the set of all sets.

(5) Less than or equal (<=) is a partial order defined on the set of real numbers.

(6) Less than or equal (<=) is a total order defined on the set of real numbers.

(7) Less than (<) is a partial order defined on the set of real numbers.

(8) Less than (<) is a total order defined on the set of real numbers.

4. (12) True or False.

(1) f (x) = 2x is onto where f: R -> R.           (Note: R is the set of real numbers)

(2) f (x) = 2x is one-to-one where f: R -> R.

(3) f(x) = x² is onto where f: R -> R.

(4) f(x) = x² is one-to-one where f: R -> R.

(5) f(x) = x² is onto where f: R -> [0, ∞).

(6) f(x) = x² is one-to-one where f: R -> [0, ∞).

5. (6) Let ℕ be the set of nonnegative integers. For each of the following sentences in first-order logic, state whether the sentence is valid, is satisfiable (but not valid), or is unsatisfiable.

(1) "x Î ℕ ($y Î ℕ (y < x)).

(2) "x Î ℕ ($y Î ℕ (y > x)).

(3) "x Î ℕ ($y Î ℕ f(x) = y).

6. (20) Are the following sets closed under the given operations? Answer yes or no. If the answer is no, please specify what the closure is.

(1) The negative integers under subtraction.

(2) The odd integers under the operation of mod 3.

(3) The positive integers under exponentiation.

(4) The finite sets under Cartesian product.

(5) The rational numbers under addition.

7. (20) True or False. If the answer is true, provide an example (Hint: use subsets of integers and real numbers) as a proof.

(1) The intersection of two countably infinite sets can be finite.

(2) The intersection of two countably infinite sets can be countably infinite.

(3) The intersection of two uncountable sets can be finite.

(4) The intersection of two uncountable sets can be countably infinite.

(5) The intersection of two uncountable sets can be uncountable.

Use the Lagrange interpolating polynomial to approximate √3 with the function f(x)= 3x-0.181and the values x0=-2, X1=-1, X2=0, X3=1 and X4=2.(Uses 4 decimal figures)

1. It has been suggested that global warming may increase the frequency of hurricanes. The table given below shows the number of major Atlantic hurricanes recorded annually before and after 1990.

Does this data is sufficient enough to claim that the number of annual hurricanes increased since 1995? Do the test at 8% significance level. To do the test, answer the following: a. Write down the null and alternative hypotheses. b. Get the excel output and answer the following: i. Fill the cell with the p-value of the test with green color ii. Fill the cell with the test statistic of the test with yellow color

Question 6

Which of the following for loops will find the largest element in the array numbers, assuming numbers has already been assigned a collection of numeric values?

Question 6 options:

Question 7

Which of the following is the correct output from this sequence of statements?

array1 = [1, 2, 3]
array2 = [2, 3]
print((array1 + array2) * 2)

Question 7 options:

Question 8

Which of the following is the correct output from this sequence of statements?

primes = [2, 3, 5, 7, 11, 13]
primes[3:] = [1, 2, 3]
print(primes[:4])

Question 8 options:

Question 9

Which of the following is the correct output from the following sequence of statements?

sequence = [1, 3, 5, 7, 9]
for i in range(len(sequence)):
sequence[i] = i + sequence[i]
print(sequence)

Question 9 options:

Question 10

Which of the following is the correct output from this sequence of statements?

numbers = [18, 27, 42, 13, 21, 8, 11]
print(max(numbers))

Question 10 options:

Find the approximate area under the curve by dividing the intervals into n subintervals and then adding up the areas of the inscribed rectangles. The height of each rectangle may be found by evaluating the function for each value of x. Your instructor will assign you n_1 = 4 and n_2 = 8.

1. y=2x√(x^2+1) Between x = 0 and x = 6 for n1 = 4, and n2 = 8

2. Find the exact area under the curve using integration y=2x√(x^2+1) Between x = 0 and x = 6

3. Explain the reason for the difference in answers.

Consider this table of values for a function:

1. How many zeroes does this function appear to have?
2. Where are those zeroes (give intervals of x-values). Use interval notation.
3. Can you be guaranteed that those are the only zeroes? Why or why not?
4. If I told you that the table represented a third degree (cubic) polynomial, is that enough to guarantee that those are the only zeroes?
5. What theorem explains your answers to # 1 through 4?