Basic Business Statistics, Student Value Edition
14th Edition
ISBN: 9780134685113
Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat
Publisher: PEARSON
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Chapter 10, Problem 66PS
a.
To determine
Test whether there is a difference in the proportion of males and females, who ordered dessert.
b.
To determine
Test whether there is a difference between the proportions of people who ordered dessert based on whether a beef entrée has been ordered.
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Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots.
Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…
In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Problem 4. Margrabe formula and the Greeks (20 pts)
In the homework, we determined the Margrabe formula for the price of an option allowing you to
swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility
σ and correlation p, the formula was given by
Fo=yo (d+)-x0Þ(d_),
where
In (±²
Ꭲ
d+
õ√T
and
σ = σ√√√2(1 - p).
дго
(a) We want to determine a "Greek" for ỡ on the option: find a formula for
θα
(b) Is
дго
θα
positive or negative?
(c) We consider a situation in which the correlation p between the two stocks increases: what
can you say about the price Fo?
(d) Assume that yo< xo and p = 1. What is the price of the option?
Chapter 10 Solutions
Basic Business Statistics, Student Value Edition
Ch. 10 - If you have samples of n1=12andn2=15, in...Ch. 10 - Assume that you have a sample of n1=8, with the...Ch. 10 - What assumptions about the two populations are...Ch. 10 - Referring to Problem 10.2, construct a 95...Ch. 10 - Prob. 5PSCh. 10 - Referring to Problem 10.2, if n1=5andn2=4, at the...Ch. 10 - When people make estimates, they are influenced by...Ch. 10 - A recent study found that 51 children who watched...Ch. 10 - Is there a difference in the satisfaction rating...Ch. 10 - Accounting Today Identified the top accounting...
Ch. 10 - The annual NFL Super Bowl is the most widely...Ch. 10 - A bank with a branch located in a commercial...Ch. 10 - Repeat Problem 10.12 (a), assuming that the...Ch. 10 - As a member of the international strategic...Ch. 10 - Repeat Problem 10.14 (a), assuming that the...Ch. 10 - Prob. 16PSCh. 10 - Brand valuations are critical to CEOs, financial...Ch. 10 - Prob. 18PSCh. 10 - Prob. 19PSCh. 10 - Nine experts rated two brands of coffee in...Ch. 10 - How do the rating of TV and Internet services...Ch. 10 - Prob. 22PSCh. 10 - How do the fares for airlines that directly...Ch. 10 - Multiple myeloma, or blood plasma cancer, is...Ch. 10 - Prob. 25PSCh. 10 - The file Concrete1 contains the compressive...Ch. 10 - Prob. 27PSCh. 10 - Prob. 28PSCh. 10 - An online survey asked 1,004 adults “if...Ch. 10 - Does Cable Video-on Demand VODD4+ increase ad...Ch. 10 - Are you an impulse shopper? A survey of 500...Ch. 10 - The Society for Human Resource Management (SHRM)...Ch. 10 - What social media tools do marketers commonly use?...Ch. 10 - Prob. 34PSCh. 10 - Prob. 35PSCh. 10 - Prob. 36PSCh. 10 - Prob. 37PSCh. 10 - Prob. 38PSCh. 10 - The following information is available is for two...Ch. 10 - In Problem 10.39, how many degrees of freedom are...Ch. 10 - In problem 10.38 and 10.39, what is the upper-tail...Ch. 10 - In Problem 10.39, what is your statistical...Ch. 10 - The following information is available for two...Ch. 10 - Prob. 44PSCh. 10 - Prob. 45PSCh. 10 - Prob. 46PSCh. 10 - A bank with a branch located in a commercial...Ch. 10 - The annual NFL Super Bowl is the most widely...Ch. 10 - Prob. 49PSCh. 10 - Prob. 50PSCh. 10 - Prob. 51PSCh. 10 - Prob. 52PSCh. 10 - Prob. 53PSCh. 10 - What is the distinction between two independent...Ch. 10 - Prob. 55PSCh. 10 - Prob. 56PSCh. 10 - Prob. 57PSCh. 10 - The American Society for Quality (ASQ) conducted a...Ch. 10 - How do private universities and public colleges...Ch. 10 - Do males and females differ in the amount of time...Ch. 10 - The file Restaurants contains the rating for food,...Ch. 10 - A Computer information systems professor is...Ch. 10 - Do social shoppers differ other online consumers...Ch. 10 - Prob. 64PSCh. 10 - Prob. 65PSCh. 10 - Prob. 66PSCh. 10 - Prob. 67PSCh. 10 - Prob. 68PSCh. 10 - Prob. 69PSCh. 10 - Referring to the results of Problems 10.67 and...
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- We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward
- The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forwardUsing the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. LOADING... Click the icon to view the Home Market Value data. Question content area bottom Part 1 Construct a frequency distribution of the errors, e Subscript iei. (Type whole numbers.) Error Frequency minus−15 comma 00015,000less than< e Subscript iei less than or equals≤minus−10 comma 00010,000 0 minus−10 comma 00010,000less than< e Subscript iei less than or equals≤minus−50005000 5 minus−50005000less than< e Subscript iei less than or equals≤0 21 0less than< e Subscript iei less than or equals≤50005000 9…arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c Overhead Costs Billable Hours345000 3000385000 4000410000 5000462000 6000530000 7000545000 8000arrow_forward
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