Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. = 0.05 for a two-tailed test.
±2.575
1.764
±1.96
±1.645
Question 2
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. = 0.09 for a right-tailed test.
±1.96
1.34
±1.96
1.34
±1.34
1.96
Question 3
Find the value of the test statistic z using z = The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 681 drowning deaths of children with 30% of them attributable to beaches.
3.01
3.01
2.85
-2.85
-3.01
Question 4
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a left-tailed test is z = -1.83.
0.0672; reject the null hypothesis
0.0336; reject the null hypothesis
0.9664; fail to reject the null hypothesis
0.0672; fail to reject the null hypothesis
Question 5
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a two-tailed test is z = -1.63.
0.1032; fail to reject the null hypothesis
0.0516; reject the null hypothesis
0.0516; fail to reject the null hypothesis
0.9484; fail to reject the null hypothesis
Question 6
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
There is not sufficient evidence to support the claim that the mean attendance is less than 694.
There is sufficient evidence to support the claim that the mean attendance is greater than 694.
There is sufficient evidence to support the claim that the mean attendance is less than 694.
There is not sufficient evidence to support the claim that the mean attendance is greater than 694.
Question 7
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A medical researcher claims that 6% of children suffer from a certain disorder. Identify the type I error for the test.
Reject the claim that the percentage of children who suffer from the disorder is different from 6% when that percentage really is different from 6%.
Reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.
Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.
Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually different from 6%.
Question 8
Find the P-value for the indicated hypothesis test. In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.
0.2843
-0.2843
0.2157
0.5686
Question 9
Find the critical value or values of based on the given information. H0: = 8.0 n = 10 = 0.01
2.088, 21.666
1.735, 23.589
23.209
21.666
Question 10
Find the critical value or values of based on the given information. H1: > 3.5 n = 14 = 0.05
22.362
22.362
5.892
24.736
23.685
5.892

1) Find the simple interest on the loan. \$1400 at 8% for 10 years.

2) Find the total amount due for the simple interest loan. \$1300 at 8% for 10 years.

3) Find the interest rate on a loan charging \$528 simple interest on a principal of \$2750 after 6 years.

4) Find the term of a loan of \$500 at 3.5% if the simple interest is \$35. .

5) Determine the amount due on the compound interest loan. (Round your answers to the nearest cent.) \$11,000 at 3% for 10 years if the interest is compounded in the following ways. (a) annually  (b) quarterly

6) Calculate the present value of the compound interest loan. (Round your answers to the nearest cent.) \$26,000 after 7 years at 5% if the interest is compounded in the following ways. (a) annually  (b) quarterly

7) Find the term of the compound interest loan. (Round your answer to two decimal places.) 5.9% compounded quarterly to obtain \$8300 from a principal of \$2000.

8) Use the “rule of 72” to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.) 9% compounded annually. Rule of 72   Exact answer

9) Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.) 15% compounded monthly. [Note: This rate is a typical credit card interest rate, often stated as 1.3% per month.]

10) Since 2007, a particular fund returned 13.7% compounded monthly. How much would a \$5000 investment in this fund have been worth after 3 years? (Round your answer to the nearest cent.)

11) In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the accumulated amount of the annuity. (Round your answer to the nearest cent.) \$4500 annually at 6% for 10 years.

12) In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the required payment for the sinking fund. (Round your answer to the nearest cent.) Monthly deposits earning 4% to accumulate \$9000 after 10 years.

13) In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) \$3500 yearly at 6% to accumulate \$100,000.

14) In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to \$5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.8%. Joe deposits \$5000 once each year, while Jill has \$96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.)

15) In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. How much must you invest each month in a mutual fund yielding 12.8% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.)

16) Calculate the present value of the annuity. (Round your answer to the nearest cent.) \$19,000 annually at 7% for 10 years.

17) Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Monthly payments on \$110,000 at 4% for 25 years.

18) Determine the payment to amortize the debt. (Round your answer to the nearest cent.) Quarterly payments on \$16,500 at 3.6% for 6 years.

19) Find the unpaid balance on the debt. (Round your answer to the nearest cent.) After 5 years of monthly payments on \$180,000 at 3% for 25 years.

20) The super prize in a contest is \$10 million. This prize will be paid out in equal yearly payments over the next 25 years. If the prize money is guaranteed by AAA bonds yielding 5% and is placed into an escrow account when the contest is announced 1 year before the first payment, how much do the contest sponsors have to deposit in the escrow account? (Round your answer to the nearest cent.)

## MAT540 Week 10 Homework

MAT540

Week 10 Homework

Chapter 6

4. Consider the following transportation problem:

From To (cost) Supply

1 2 3

A \$ 6 \$ 9 \$100 130

B 12 3 5 70

C 4 8 11 100

Demand 80 110 60

Formulate this problem as a linear programming model and solve it by using the computer.

6. Consider the following transportation problem:

From To (cost) Supply

1 2 3

A \$ 6 \$ 9 \$ 7 130

B 12 3 5 70

C 4 8 11 100

Demand 80 110 60

Solve it by using the computer.

36. World Foods, Inc., imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver the products to Norfolk, New York and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are then distributed to specialty foods stores and sold through catalogs. The shipping costs (\$/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are provided in the following table:

From To (cost) Supply

4. Norfolk 5. New York 6. Savannah

1. Hamburg \$420 \$390 \$610 55
2. Marseilles 510 590 470 78
3. Liverpool 450 360 480 37

The transportation costs (\$/1,000 lb.) from each U.S. city of the three distribution centers and the demands (1,000 lb.) at the distribution centers are as follows:

Warehouse Distribution Center

7. Dallas 8. St. Louis 9. Chicago
4. Norfolk \$ 75 \$ 63 \$ 81
5. New York 125 110 95
6. Savannah 68 82 95

Demand 60 45 50

Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs.

48. The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table:

Region (days)

Sales-person A B C D E

1 17 10 15 16 20

2 12 9 16 9 14

3 11 16 14 15 12

4 14 10 10 18 17

5 13 12 9 15 11

Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time.

# MAT540 Week 10 Homework Chapter 6 4. Consider the following transportation problem: From To (cost) Supply 1 2 3  A \$ 6 \$ 9 \$100 130 B 12 3 5 70 C 4 8 11 100 Demand 80 110 60  Formulate this problem as a linear programming model and solve it by using the computer. 6. Consider the following transportation problem: From To (cost) Supply 1 2 3  A \$ 6 \$ 9 \$ 7 130 B 12 3 5 70 C 4 8 11 100 Demand 80 110 60  Solve it by using the computer. 36. World Foods, Inc., imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver the products to Norfolk, New York and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are then distributed to specialty foods stores and sold through catalogs. The shipping costs (\$/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are provided in the following table: From To (cost) Supply 4. Norfolk 5. New York 6. Savannah  1. Hamburg \$420 \$390 \$610 55 2. Marseilles 510 590 470 78 3. Liverpool 450 360 480 37 The transportation costs (\$/1,000 lb.) from each U.S. city of the three distribution centers and the demands (1,000 lb.) at the distribution centers are as follows: Warehouse Distribution Center 7. Dallas 8. St. Louis 9. Chicago 4. Norfolk \$ 75 \$ 63 \$ 81 5. New York 125 110 95 6. Savannah 68 82 95 Demand 60 45 50 Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs. 48. The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table: Region (days) Sales-person A B C D E 1 17 10 15 16 20 2 12 9 16 9 14 3 11 16 14 15 12 4 14 10 10 18 17 5 13 12 9 15 11 Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time.

Question 1

A ‘rare’ outcome, due to an extreme value found for the sample mean relative to the population mean, signifies that the null hypothesis should be:

a.         retained

b.         rejected

c.         accepted

d.         none of the above

Question 2

To express a sample mean as a Z value:

a.         subtract the hypothesized population mean.

b.         subtract the hypothesized population mean and divide by the standard deviation.

c.         subtract the hypothesized population mean and divide by the standard error of the mean.

d.         subtract the hypothesized population mean and divide by the variance.

Question 3

Given critical z values of ±1.96 and an observed z value of -2.40, the appropriate decision is to:

a.         neither retain nor reject, but conduct another investigation

b.         neither retain nor reject, but increase the size of the sample

c.         reject the null hypothesis

d.         retain the null hypothesis

Question 4

Given an observed difference between a sample mean of 42 and a hypothesized population mean of 50, you:

a.         must determine whether this observed difference can reasonably be attributed to chance

b.         can retain, but not accept, the null hypothesis

c.         can conclude that the alternative hypothesis is true

d.         can conclude that the null hypothesis is true

Question 5

A decision to reject the null hypothesis implies that:

a.         there is a lack of support for the alternative hypothesis

b.         there is support for the alternative hypothesis

c.         the sample is probably not representative

d.         the sample size is probably too small

e.         none of the above

Question 6

Compared to a two-tailed hypothesis test, a one-tailed test is more likely to detect a:

a.         true null hypothesis in the direction of concern

b.         false null hypothesis

c.         false null hypothesis in the direction of concern

d.         true null hypothesis

Question 7

When the rejection of a true null hypothesis would have unusually disastrous consequences, it is best to set your level of significance equal to:

a.         .10

b.         .05

c.         .01

d.         .001

Question 8

If your observed sample mean were exactly equal to your population mean (assuming some moderate variation in both the sample and the population), then your z value would be:

1.         1.96

2.         1.65

3.         2.58

4.         0

5.         not enough information to determine

Question 9

In an experiment to determine whether TV cartoons produce more aggressive behavior in grade school children, the null hypothesis would state that TV cartoons have:

a.         a statistically significant effect on aggressive behavior

b.         only a slight effect on aggressive behavior

c.         an effect on aggressive behavior

d.         no effect on aggressive behavior

Question 10

If the null hypothesis is in reality false, and the z value of the randomly selected sample doesn’t deviate beyond the critical z value, the null hypothesis will be:

1.         correctly retained

2.         correctly rejected

3.         incorrectly retained

4.         incorrectly rejected

Question 11

Two ways to increase the likelihood of detecting a real effect are to _______ sample size and to _______ alpha.

a.         decrease; decrease

b.         decrease; increase

c.         increase; decrease

d.         increase; increase

Question 12

You’re testing a new vitamin pill that could save many lives if it works even a little bit, and would do no harm even if it did not have any real effect. Given that there is often a trade off between risking Type I and Type II error, which type should you concentrate on minimizing in this situation?

a.         Type I error

b.         Type II error

c.         both Type I and Type II error are equally bad

d.         Type III error; I don’t know what it is, but I don’t like it

Given an observed difference between a sample mean of 42 and a hypothesized population mean of 50, you:
a. must determine whether this observed difference can reasonably be attributed to chance
b. can retain, but not accept, the null hypothesis
c. can conclude that the alternative hypothesis is true
d. can conclude that the null hypothesis is true

A decision to reject the null hypothesis implies that:
a. there is a lack of support for the alternative hypothesis
b. there is support for the alternative hypothesis
c. the sample is probably not representative
d. the sample size is probably too small
e. none of the above

Compared to a two-tailed hypothesis test, a one-tailed test is more likely to detect a:
a. false null hypothesis
b. false null hypothesis in the direction of concern
c. true null hypothesis
d. true null hypothesis in the direction of concern

When the rejection of a true null hypothesis would have unusually disastrous consequences, it is best to set your level of significance equal to:
a. .10
b. .05
c. .01
d. .001

If your observed sample mean were exactly equal to your population mean (assuming some moderate variation in both the sample and the population), then your z value would be:
1. 1.96
2. 1.65
3. 2.58
4. 0
5. not enough information to determine

In an experiment to determine whether TV cartoons produce more aggressive behavior in grade school children, the null hypothesis would state that TV cartoons have:
a. a statistically significant effect on aggressive behavior
b. only a slight effect on aggressive behavior
c. an effect on aggressive behavior
d. no effect on aggressive behavior

If the null hypothesis is in reality false, and the z value of the randomly selected sample doesn’t deviate beyond the critical z value, the null hypothesis will be:
1. correctly retained
2. correctly rejected
3. incorrectly retained
4. incorrectly rejected

Two ways to increase the likelihood of detecting a real effect are to _______ sample size and to _______ alpha.
a. decrease; decrease
b. increase; increase
c. decrease; increase
d. increase; decrease

You’re testing a new vitamin pill that could save many lives if it works even a little bit, and would do no harm even if it did not have any real effect. Given that there is often a trade off between risking Type I and Type II error, which type should you concentrate on minimizing in this situation?
a. Type I error
b. Type II error
c. both Type I and Type II error are equally bad
d. Type III error; I don’t know what it is, but I don’t like it.

Question 1. 1. According to the following graphic, X and Y have _________.
(Points : 3)
strong negative correlation
virtually no correlation
strong positive correlation
moderate negative correlation
weak negative correlation

Question 2. 2. A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a function of batch size (the number of boards produced in one lot or batch). The independent variable is ______. (Points : 3)
batch size
unit variable cost
fixed cost
total cost
total variable cost

Question 3. 3. A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch). The intercept of this model is the ______. (Points : 3)
batch size
unit variable cost
fixed cost
total cost
total variable cost

Question 4. 4. If x and y in a regression model are totally unrelated, _______. (Points : 3)
the correlation coefficient would be -1
the coefficient of determination would be 0
the coefficient of determination would be 1
the SSE would be 0
the MSE would be 0sQuestion 5. 5. A manager wishes to predict the annual cost (y) of an automobile based on the number of miles (x) driven. The following model was developed: y = 1,550 + 0.36x.
If a car is driven 10,000 miles, the predicted cost is ____________. (Points : 3)
2090
3850
7400
6950
5150Question 6. 6. A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch), production plant (Kingsland, and Yorktown), and production shift (day and evening). In this model, “shift” is ______. (Points : 3)
a response variable
an independent variable
a quantitative variable
a dependent variable
a constant

Question 7. 7. A multiple regression analysis produced the following tables: Predictor
Coefficients
Standard Error
t Statistic
p-valueIntercept
The regression equation for this analysis is ____________. (Points : 3)

7. A multiple regression analysis produced the following tables:

 Predictor Coefficients Standard Error t Statistic p-value Intercept 616.6849 154.5534 3.990108 0.000947 x1 -3.33833 2.333548 -1.43058 0.170675 x2 1.780075 0.335605 5.30407 5.83E-05

 Source df SS MS F p-value Regression 2 121783 60891.48 14.76117 0.000286 Residual 15 61876.68 4125.112 Total 17 183659.6

These results indicate that ____________. (Points : 3)
none of the predictor variables are significant at the 5% level
each predictor variable is significant at the 5% level
x1 is the only predictor variable significant at the 5% level
x2 is the only predictor variable significant at the 5% level
the intercept is not significant at the 5% level

Question 9. 9. A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area, number of bedrooms, number of bathrooms, age of the house, and central heating (yes, no). The response variable in this model is _______. (Points : 3)
heated area
number of bedrooms
market value
central heating
residential houses

Question 10. 10. In regression analysis, outliers may be identified by examining the ________. (Points : 3)
coefficient of determination
coefficient of correlation
p-values for the partial coefficients
residuals
R-squared value

## Q8a

Which one of the following statements is correct?

 To maximize the value of a firm you need to maximize the firm’s WACC. A Chapter 7 bankruptcy is a legal process for reorganizing a firm. Investors can use homemade leverage to offset firm leverage. To maximize the value of a firm you need to borrow as much as you can.

2.     A firm has 100,000 shares of stock outstanding. The firm is considering borrowing \$1.3 million at 7.5% interest and using the loan proceeds to repurchase 25,000 shares of stock. What is the value of the firm? Ignore taxes.

 \$5.20 million \$5.98 million \$6.50 million \$7.25 million

3.     A firm has a debt-equity ratio of 1.0. The required return on the firm’s assets is 16.1% and the pre-tax cost of debt is 9.1%. Ignore taxes. What is the firm’s cost of equity?

 15.3% 18.2% 23.1% 21.7%

4.     A company is an all-equity firm that has projected earnings before interest and taxes (EBIT) of \$500,000 forever. The current cost of equity is 15% and the tax rate is 33%. The company is in the process of issuing \$1.5 million of bonds at par that carry a 6% annual coupon. What is the unlevered value of the firm (in millions)? (Note: You should use MM capital structure model with corporate taxes, but without personal taxes and bankruptcy costs.)

 \$2.05 million \$2.23 Million \$2.56 Million \$2.85 Million

5.     From Question 4, what is the levered value of the firm (in millions)?_______

 \$2.05 million \$2.36 million \$2.56 million \$2.73 million

## math

From the time of early studies by Sir Francis Galton in the late nineteenth century linking it with mental ability, the cranial capacity of the human skull has played an important role in arguments about IQ, racial differences, and evolution, sometimes with serious consequences.  (See, for example, S.J. Gould, “The Mismeasure of Man,” 1996.)

Suppose that the mean cranial     capacity measurement for modern, adult males is

1041 cc (cubic centimeters).

Complete    the following statements about the distribution of cranial capacity measurements for modern, adult males.

(a) According to Chebyshev’s theorem, at least ?56%75%84%89% of the measurements lie within 2 standard deviations of the mean, 1041cc.

(b) Suppose that the distribution is bell-shaped.  If approximately 99.7% of the measurements lie between 309 cc and 1773 cc, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is .

## Intermediate Computations

Random and independent samples of  recent prime time airings from each of two major networks have been considered. The first network aired a mean of  commercials during prime time, with a standard deviation of  commercials. The second network aired a mean of  commercials, with a standard deviation of  commercials. As the sample sizes are quite large, the population standard deviations can be estimated using the sample standard deviations. Construct a  confidence interval for , the difference between the mean number of commercials  aired during prime time by the first network and the mean number of commercials  aired during prime time by the second network. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)

What is the lower limit of the 99% confidence interval?

What is the upper limit of the 99% confidence interval?