7. A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to "win" the tickets. There are 8 secretaries, 7 consultants and 5 partners in the firm. Which of the following statements is not true? A) The probability of a secretary winning a ticket on the first draw is 8/20. B) The probability of a secretary winning a ticket on the second draw given that a consultant won a ticket on the first draw is 7/19. C) The probability of a consultant winning a ticket on the first draw is 7/20. D) The probability of a partner winning a ticket on the second draw given that a secretary won a ticket on the first draw is 5/19.

2. A random sample of 395 people were surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table:
    High School   Bachelors   Masters   Ph.d.   Total
Female   60   54   46   41   201
Male   40   44   53   57   194
Total   100   98   99   98   395
a. Are gender and education level dependent at 5% level of significance? (6mks)
b.State and explain two methods of studying correlation                    (4mks

Statistice inferential question

3. [] The executive is also worried that the bank is losing ground to its major competitor, the Everglades Bank. So the bank executive asked you to determine whether Everglades Bank processes mortgages faster than First National. To conduct this hypothesis test you also collect a random sample of 108 mortgage processing times from Everglades Bank. These data are also located in your Excel file. a) Should your alternative be left-sided, right-sided, or two-sided? Explain. b) State your null and alternative hypotheses using correct symbols and notation. Make sure to clearly identify the populations. c) Conduct a two-sample t-test for comparing the difference between two means. Include Excel calculations in your Word document. d) State the P-value and give the conclusion in context using a significance level of 0.05.

Data to use here :

Number of Days to Process Mortgage Applications

First National 7 8 2 5 6 7 6 4 8 2 5 9 6 3 7 6 7 9 8 8 5 8 5 6 6 9 7 10 8 9 6 6 11 5 7 4 7 6 12 7 10 5 6 6 6 5 4 4 8 9 3 3 10 5 3 11 7 5 6 2 9 13 7 7 6 4 5 9 3 9 9 8 5 7 2 5 10 11 8 10 5 7 4 14 8 4 7 6 8 5 8 2 5 5 8 6 9 6 5 11 9 6 6 8 12 8 10 6

Everglades Bank 4 8 7 4 5 4 10 10 3 9 8 4 8 9 8 9 8 3 8 4 4 7 6 7 10 9 10 3 9 3 7 7 9 9 5 7 6 9 7 5 4 7 7 10 5 8 3 8 5 5 3 6 2 4 7 2 7 3 4 8 5 5 9 5 6 5 8 7 4 7 2 6 2 6 10 6 2 8 5 8 7 10 9 5 10 4 6 3 7 12 8 5 6 6 8 8 4 4 8 6 6 6 7 11 3 7 7 4

If you have two groups. The first group got some similar numbers but over a wider range of numbers. The second group got less similar numbers but the numbers were in a closer range. Which group had the much more precise results? The group with similar numbers but over a wider range or the group with only one match but all numbers were very close together?

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.

(a) Conduct a test of independence to determine whether hours of sleep are independent of age.

State the null and alternative hypotheses:

A. H₀: Hours of sleep per night is independent of age.
H_a: Hours of sleep per night is not independent of age.

B. H₀: Hours of sleep per night is mutually exclusive from age.
H_a: Hours of sleep per night is not mutually exclusive from age.    

C. H₀: Hours of sleep per night is not independent of age.
H_a: Hours of sleep per night is independent of age.

D. H₀: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.
H_a: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups.

Find the value of the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

Using a 0.05 level of significance, what is your conclusion?

A. Reject H₀. We conclude that hours of sleep per night and age are not independent.

B. Do not reject H₀. We cannot conclude that hours of sleep per night and age are not independent.     

C. Reject H₀. We cannot conclude that hours of sleep per night and age are independent.

D. Do not reject H₀. We conclude that hours of sleep per night and age are independent.

(b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Fewer than 6: ____%

6 to 6.9: _____%

7 to 7.9: _____%

8 or more: _____%

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.

(a)

Conduct a test of independence to determine whether hours of sleep are independent of age.

State the null and alternative hypotheses.

H₀: Hours of sleep per night is not independent of age.
H_a: Hours of sleep per night is independent of age.H₀: Hours of sleep per night is mutually exclusive from age.
H_a: Hours of sleep per night is not mutually exclusive from age.    H₀: Hours of sleep per night is independent of age.
H_a: Hours of sleep per night is not independent of age.H₀: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.
H_a: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups.

Find the value of the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We conclude that hours of sleep per night and age are independent.Reject H₀. We conclude that hours of sleep per night and age are not independent.    Reject H₀. We cannot conclude that hours of sleep per night and age are independent.Do not reject H₀. We cannot conclude that hours of sleep per night and age are not independent.

(b)

What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Fewer than 6 %6 to 6.9 %7 to 7.9 %8 or more %

a) Using the empirical rule, 95% of female promotional customer ages should be between what two values? Either show work or explain how your answer was calculated.

b)Using the empirical rule, 68% of items purchased should be between what two values? Either show work or explain how your answer was calculated.    

Paymore Products places orders for goods equal to 75% of its sales forecast in the next quarter which has been provided in the below table.

On average, one-third of sales are collected in the quarter that they are sold, and two-thirds are collected in the following quarter. Assume that sales in the last quarter of the previous year were $346. Also, one third of the orders are paid for in the current month and then two thirds of the next quarter's orders are paid in advance. Assuming that Paymore’s labor and administrative expenses are $75 per quarter and that interest on long-term debt is $50 per quarter, work out the net cash flow for Paymore for the coming year using the below table.

1. As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $51,500. Its operating costs are $20,200 a year, but in five years the machine will require a $19,900 overhaul. Thereafter operating costs will be $30,100 until the machine is finally sold in year 10 for $5,150.

The older machine could be sold today for $25,100. If it is kept, it will need an immediate $20,500 overhaul. Thereafter operating costs will be $29,900 a year until the machine is finally sold in year 5 for $5,150.   

Both machines are fully depreciated for tax purposes. The company pays tax at 35%. Cash flows have been forecasted in real terms. The real cost of capital is 11%.

a. Calculate the equivalent annual costs for selling the new machine and for selling the old machine.

2. Hayden Inc. has a number of copiers that were bought four years ago for $29,000. Currently maintenance costs $2,900 a year, but the maintenance agreement expires at the end of two years and thereafter the annual maintenance charge will rise to $8,900. The machines have a current resale value of $8,900, but at the end of year 2 their value will have fallen to $4,400. By the end of year 6 the machines will be valueless and would be scrapped.

Hayden is considering replacing the copiers with new machines that would do essentially the same job. These machines cost $34,000, and the company can take out an eight-year maintenance contract for $1,200 a year. The machines will have no value by the end of the eight years and will be scrapped.

Both machines are depreciated by using seven-year MACRS, and the tax rate is 40%. Assume for simplicity that the inflation rate is zero. The real cost of capital is 8%.

a. Calculate the equivalent annual cost, if the copiers are: (i) replaced now, (ii) replaced two years from now, or (iii) replaced six years from now.

3.

The president’s executive jet is not fully utilized. You judge that its use by other officers would increase direct operating costs by only $33,000 a year and would save $100,000 a year in airline bills. On the other hand, you believe that with the increased use the company will need to replace the jet at the end of three years rather than four. A new jet costs $1.23 million and (at its current low rate of use) has a life of seven years. Assume that the company does not pay taxes. All cash flows are forecasted in real terms. The real opportunity cost of capital is 7%.

a. Calculate the equivalent annual cost of a new jet.

b. Calculate the present value of the additional cost of replacing the jet one year earlier than under its current usage.

c. Calculate the present value of the savings.

1.

Complete the following table and calculate the inflation rates.

  % (precise to 1 decimal point, e.g., 9.4%)

  % (precise to 1 decimal point, e.g., 9.4%)

2.

Suppose a community has a total population of 500, of which 100 are youth under the age of 16, 100 work 40 hours per week, 100 work 1-39 hours per week, 100 have been looking for work in the past four weeks, 50 are retired, 25 are college students, and 25 stay home voluntarily.

What is the labor force?   

What is the working age population?   

What is the unemployment rate?   % (e.g., 12%)

What is the labor force participation rate?   % (e.g., 12%)

3.

An economy produces only fish and oranges. The table below shows the quantity produced and their prices in 2007 and 2008. What are the nominal GDP in 2007 and 2008? And what is the real GDP in 2008 using prices in 2007? (base year = 2007)

What is the real GDP in 2008?

4.

Excess reserves refer to the remaining cash reserves financial institutions have after satisfying the reserve requirement. Suppose a bank receives one and only one cash deposit of $6,000,000, and the current required reserve ratio is 10%. What is the excess reserves?

• A.

  5,400,000

• B.

  3,600,000

• C.

  4,000,000

• D.

  4,500,000

5.Shannon made $50,000 last year and received a $10,000 raise this year for her excellence at work. With the additional income, she spent $6,000 more this year. What is the marginal propensity to consume (MPC) for Shannon?

• A. 70%

• B. 50%

• C. 60%

• D. 40%

6.In the previous question, what is Shannon's marginal propensity to save (MPS)?

• A. 40%

• B. 60%

• C. 10%

• D. 30%

7.Suppose banks keep cash reserves as much as 5% of their deposits (currency drain ratio), and the current required reserve ratio is 10%. What is the money multiplier?

multiplier = (1 + CDR) / (RRR + CDR)

• A. 7

• B. 3

• C. 6

• D. 4

8.Suppose the U.S. real GDP in 2008 is $14 trillion, price level is 2, and velocity of circulation is 4. What is the quantity of money in the economy?

• A. 28 trillion

• B. 7 trillion

• C. 14 trillion

• D. 4 triliion