An observational study of 19 managers from a medium-sized manufacturing plant investigated which activities successful managers perform (Journal of Applied Behavioral Science, August 1985). To measure success, the researchers devised an index based on the manager's length of time in the organization and his or her level within the firm; the higher the index, the more successful the manager. The table on the following page presents data that can determine whether managerial success is related to the extensiveness of a manager's network-building interactions with people outside the manager's work unit. Such interactions include phone and face-to-face meetings with customers and suppliers, attending outside meetings, and doing public relations work.

Manager	Manager Success Index, $y$	Number of Interactions with Outsiders, $x$
1	40	12
2	73	71
3	95	70
4	60	81
5	81	43
6	27	50
7	53	42
8	66	18
9	25	35
10	63	82
11	70	20
12	47	81
13	80	40
14	51	33
15	32	45
16	50	10
17	52	65
18	30	20
19	42	21

i. In the context of this problem, decide the value of $x$ for which the associated prediction interval for $y$ is the narrowest.

Internal auditing of invoices. A firm's president, vice presidents, department managers, and others use financial data generated by the firm's accounting system to help them make decisions regarding such things as pricing, budgeting, and plant expansion. To provide reasonable certainty that the system provides reliable data, internal auditors periodically perform various checks of the system (Horngren, Foster, and Datar, Cost Accounting: A Managerial Emphasis, 2005). Suppose an internal auditor is interested in determining the proportion of sales invoices in a population of 5,000 sales invoices for which the "total sales" figure is in error. She plans to estimate the true proportion of invoices in error based on a random sample of size 100. Assume that the population of invoices is numbered from 1 to 5,000 and that every invoice ending with a 0 is in error (i.e., 10% are in error). Use a random number generator to draw a random sample of 100 invoices from the population of 5,000 invoices. For example, random number 456 stands for invoice number 456. List the invoice numbers in your sample and indicate which of your sampled invoices are in error (i.e., those ending in a 0).

Watson Corporation grants 20,000 stock options to its managerial employees on December 31, 2013, to purchase 20,000 shares of its $10 par value common stock for$25 per share. The market price of a share of common stock on this date is $25 per share. Employees must work for another three years before they can exercise the options. An option-pricing model indicates that the value of these options on the grant date is$75,000. On April 30, 2017, holders of 15,000 options exercise their options at a time when the market price of the stock is $30 per share. On September 15, 2017, holders of the remaining options exercise them at a time when the market price of the stock is$38 per share.

Present journal entries to record these transactions on December 31, 2014, 2015, and 2016; on April 30, 2017; and on September 15, 2018. Assume that the firm receives any benefits of the stock option plan during 2015, 2016, and 2017 and that the firm reports on a calendar-year basis. Ignore income tax effects.

Suppose a body has a force of $10$ pounds acting on it to the right, $25$ pounds acting on it $-135^{\circ}$ from the horizontal, and $5$ pounds acting on it directed $150^{\circ}$ from the horizontal. What single force is the resultant force acting on the body?

Taylor Marina has 300 available slips that rent for $800 per season. Payments must be made in full by the start of the boating season, April 1, 2021. The boating season ends October 31, and the marina has a December 31 year-end. Slips for future seasons may be reserved if paid for by December 31, 2021. Under a new policy, if payment for 2022 season slips is made by December 31, 2021, a 5% discount is allowed. If payment for 2023 season slips is made by December 31, 2021, renters get a 20% discount (this promotion hopefully will provide cash flow for major dock repairs).

On December 31, 2020, all 300 slips for the 2021 season were rented at full price. On December 31, 2021, 200 slips were reserved and paid for the 2022 boating season, and 60 slips were reserved and paid for the 2023 boating season.

Instructions

a. Prepare the appropriate journal entries for December 31, 2020, and December 31, 2021.

b. Assume the marina operator is unsophisticated in business. Explain the managerial significance of the above accounting to this person.

Final exam scores for a sample of 20 students in a managerial accounting class are shown.

(a) At $\alpha = .05$, is there a difference in the population median scores on the two exams? Make an Excel worksheet for your Wilcoxon signed-rank test calculations and check your work by using MegaStat or a similar computer package.

(b) Perform a two-tailed parametric t test for paired two-sample means by using Excel or MegaStat. Do you get the same decision?

During the 1980s, the controversial economist Arthur Laffer promoted the idea that tax increases lead to a reduction in government revenue. Called supply-side economics, the theory uses functions such as

$$f(x)=\frac{80 x-8000}{x-110}, 30 \leq x \leq 100 .$$

This function models the government tax revenue, $f(x)$, in tens of billions of dollars, in terms of the tax rate, $x$. The graph of the function is shown. It illustrates tax revenue decreasing quite dramatically as the tax rate increases. At a tax rate of (gasp) $100 \%$, the government takes all our money and no one has an incentive to work. With no income earned, zero dollars in tax revenue is generated.

a. Find and interpret $f(40)$. Identify the solution as a point on the graph of the function.

b. Rewrite the function by using long division to perform

$$(80 x-8000) \div(x-110)$$

Then use this new form of the function to find $f(40)$. Do you obtain the same answer as you did in part (a)?

c. Is $f$ a polynomial function? Explain your answer.

You've just kicked a rock, and it is now sliding across the ground about $2$ meters in front of you. Which of these are forces acting on the rock? Include all that apply.
A. Gravity, acting downward
B. The normal force, acting upward
C. The force of the kick, acting in the direction of motion
D. Friction, acting opposite the direction of motion
E. Air resistance, acting opposite the direction of motion

A managerial decision problem. A direct-mail company assembles and stores paper products (envelopes, letters, brochures, order cards, etc.) for its customers. The company estimates the total number of pieces received in a shipment by calculating the weight per piece and then weighing the entire shipment. The company is unsure whether the sample of pieces used to estimate the mean weight per piece should be drawn from a single carton or whether it is worth the extra time required to pull a few pieces from several cartons. To aid management in making a decision, eight brochures were removed from each of the five cartons of a typical shipment and weighed. The weights (in pounds) are shown in the table.

a. Identify the response, factor(s), treatments, and experimental units.

Final exam scores for a sample of 20 students in a managerial accounting class are shown. (a) At $\alpha=.05$, is there a difference in the population median scores on the two exams? Make an Excel worksheet for your Wilcoxon signed-rank test calculations and check your work by using MegaStat or a similar computer package. (b) Perform a two-tailed parametric $t$ test for paired two-sample means by using Excel or MegaStat. Do you get the same decision?

$$\begin{array}{ccccccccc} \text { Student } & \text { Exam 1 } & \text { Exam 2 } & \text { Student } & \text { Exam 1 } & \text { Exam 2 } & \text { Student } & \text { Exam 1 } & \text { Exam 2 } \\ \hline 1 & 70 & 81 & 8 & 71 & 69 & 15 & 59 & 68 \\ 2 & 74 & 89 & 9 & 52 & 53 & 16 & 54 & 47 \\ 3 & 65 & 59 & 10 & 79 & 84 & 17 & 75 & 84 \\ 4 & 60 & 68 & 11 & 84 & 96 & 18 & 92 & 100 \\ 5 & 63 & 75 & 12 & 95 & 96 & 19 & 70 & 81 \\ 6 & 58 & 77 & 13 & 83 & 99 & 20 & 54 & 58 \\ 7 & 72 & 82 & 14 & 81 & 76 & & & \end{array}$$

An observational study of 19 managers from a medium-sized manufacturing plant investigated which activities successful managers perform (Journal of Applied Behavioral Science, August 1985). To measure success, the researchers devised an index based on the manager's length of time in the organization and his or her level within the firm; the higher the index, the more successful the manager. The table on the following page presents data that can determine whether managerial success is related to the extensiveness of a manager's network-building interactions with people outside the manager's work unit. Such interactions include phone and face-to-face meetings with customers and suppliers, attending outside meetings, and doing public relations work.

c. Find $s$ for your prediction equation. Analyze the standard deviation $s$ in the context of this problem.

The condition of equilibrium is when the sum of the forces acting on a body is the zero vector. Suppose a body has a force of $2$ pounds acting on it to the right, $5$ pounds acting on it upward, and $3$ pounds acting on it $45^{\circ}$ from the horizontal. What single force is needed to produce a state of equilibrium in the body?

Select a nearby company. Arrange an interview for your team with a managerial accountant, a controller, or another accounting/finance officer of the company. Requirements Before your team conducts the interview, research the company and answer the following questions:

1. Is this a service, merchandising, or manufacturing company? What is its primary product or service?
2. What are some possible fixed costs this company incurs?
3. What are some possible variable costs this company incurs?
4. Select one of the company's products or services. Estimate the unit contribution margin for the product or service. At the interview, ask the above questions and compare your ream's answers to the company's answers. Then ask the following questions:
5. H ow does the company determine the sales prices of products and services?
6. What is the company's cost structure? Does the company have relatively high or low fixed costs?
7. What is the company's sales mix? Has the sales mix changed recently? If so, what caused the change? Your ream should summarize your findings in a short paper. Provide any exhibits that enhance your explanations. Provide proper references and a works cited page.

Phil and Cathy are roommates who are taking the same economics class. This morning Phil wakes up and is trying to decide whether to go to class or not. He knows that if Cathy is going to go to class he will hear her fixing herself breakfast. Cathy knows that Phil may or may not go to class depending on what she does. The timing of their decisions and their respective payoffs are as represented by the diagram below, where choosing the upper path means go to class and choosing the lower path means don’t go to class. Cathy makes her decision first and Phil waits to see what she has decided before making his decision. If the payoffs for each are as shown, what is the equilibrium of this game?