Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 11, Problem 3CS
Dr. Penelope Nicholls is interested in exploring a possible connection between high plasma homocysteine (a toxic amino acid created by the body as it metabolizes protein) levels and cardiac hypertrophy (enlargement of the heart) in humans. Because there are many complex relationships among human characteristics, it will be difficult to answer her research question due to a significant risk that confounding factors will cloud her inferences. She wants to be sure that any differences in cardiac hypertrophy are due to high plasma homocysteine levels and not to other factors. Consequently, she needs to design her experiment carefully so that she controls lurking variables to the extent possible. Therefore, she decides to design a two-sample experiment with independent sampling: one group will be the experimental group, the other a control group. Knowing that many factors can affect the degree of cardiac hypertrophy (the response variable), Dr. Nicholls controls these factors by randomly assigning the experimental units to the experimental or control group. She hopes the randomization will result in both groups having similar characteristics.
In her preliminary literature review, Dr. Nicholls uncovered an article in which the authors hypothesized that there might be a relationship between high plasma homocysteine levels in patients with end-stage renal disease (ESRD) and cardiac hypertrophy. She has asked you, as her assistant, to review this article.
Upon reading the article, you discover that the authors used a nonrandom process to select a control group and an ESRD group. The researchers enlisted 75 stable ESRD patients into their study, all on hemodialysis for between 6 and 312 months. The control group subjects were chosen so as to eliminate any intergroup differences in terms of mean blood pressure (BP) and gender. In an effort to minimize situational contaminants, all physical and biochemical measurements were made after an overnight fast. The results for the control and ESRD groups are reproduced in the tables below.
3. Detail any assumptions and the rationale behind making them that you made while carrying out your analysis. Is there any additional information that you would like to have? Explain. Are there any additional statistical procedures that you think might be useful for analyzing these data? Explain.
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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 11 Solutions
Fundamentals of Statistics (5th Edition)
Ch. 11.1 - A sampling method is _____ when the individuals...Ch. 11.1 - A sampling method is _____ when the individuals...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - In Problems 38, determine whether the sampling is...Ch. 11.1 - Prob. 8AYUCh. 11.1 - In Problems 912, conduct each test at the = 0.05...Ch. 11.1 - In Problems 912, conduct each test at the = 0.05...
Ch. 11.1 - In Problems 912, conduct each test at the = 0.05...Ch. 11.1 - In Problems 912, conduct each test at the = 0.05...Ch. 11.1 - In Problems 1316, construct a confidence interval...Ch. 11.1 - Prob. 14AYUCh. 11.1 - In Problems 1316, construct a confidence interval...Ch. 11.1 - In Problems 1316, construct a confidence interval...Ch. 11.1 - NW Prevnar The drug Prevnar is a vaccine meant to...Ch. 11.1 - Prevnar Part 2 In randomized, double-blind...Ch. 11.1 - Prob. 19AYUCh. 11.1 - Views on the Death Penalty The Pew Research Group...Ch. 11.1 - NW Tattoos The Harris Poll conducted a survey in...Ch. 11.1 - Body Mass Index The body mass index (BMI) of an...Ch. 11.1 - Public Cell Phone Conversations Researchers at...Ch. 11.1 - Prob. 24AYUCh. 11.1 - Side Effects In clinical trials of the allergy...Ch. 11.1 - Practical versus Statistical Significance In...Ch. 11.1 - Prob. 27AYUCh. 11.1 - Prob. 28AYUCh. 11.1 - Deficit Reduction In the Sullivan Statistics...Ch. 11.1 - Prob. 30AYUCh. 11.1 - Prob. 31AYUCh. 11.1 - Prob. 32AYUCh. 11.1 - Prob. 33AYUCh. 11.1 - Prob. 34AYUCh. 11.1 - Prob. 35AYUCh. 11.1 - Putting It Together: Salk Vaccine On April 12,...Ch. 11.1 - Why do we use a pooled estimate of the population...Ch. 11.1 - Explain the difference between an independent and...Ch. 11.2 - A researcher wants to show the mean from...Ch. 11.2 - A researcher wants to show the mean from...Ch. 11.2 - In Problems 3 and 4, assume that the differences...Ch. 11.2 - a. Determine di = Xi Yi for each pair of data. b....Ch. 11.2 - Naughty or Nice? An experiment was conducted in...Ch. 11.2 - Caffeine-Enhanced Workout? Since its removal from...Ch. 11.2 - NW Muzzle Velocity The following data represent...Ch. 11.2 - Reaction Time In an experiment conducted online at...Ch. 11.2 - Prob. 9AYUCh. 11.2 - Secchi Disk A Secchi disk is an 8-inch-diameter...Ch. 11.2 - Getting Taller? To test the belief that sons are...Ch. 11.2 - Prob. 12AYUCh. 11.2 - Prob. 13AYUCh. 11.2 - Car Rentals The following data represent the daily...Ch. 11.2 - DUI Simulator To illustrate the effects of driving...Ch. 11.2 - Prob. 16AYUCh. 11.2 - Prob. 17AYUCh. 11.2 - Putting It Together: Glide Testing You are a...Ch. 11.3 - In Problems 16, assume that the populations are...Ch. 11.3 - In Problems 16, assume that the populations are...Ch. 11.3 - In Problems 16, assume that the populations are...Ch. 11.3 - In Problems 16, assume that the populations are...Ch. 11.3 - In Problems 16, assume that the populations are...Ch. 11.3 - In Problems 16, assume that the populations are...Ch. 11.3 - Elapsed Time to Earn a Bachelors Degree A...Ch. 11.3 - Sugary Beverages It has been reported that...Ch. 11.3 - Prob. 9AYUCh. 11.3 - Walking in the Airport, Part II Do business...Ch. 11.3 - Priming Two Dutch researchers conducted a study in...Ch. 11.3 - Prob. 12AYUCh. 11.3 - NW Ramp Metering Ramp metering is a traffic...Ch. 11.3 - Prob. 14AYUCh. 11.3 - Bacteria in Hospital Carpeting Researchers wanted...Ch. 11.3 - Visual versus Textual Learners Researchers wanted...Ch. 11.3 - Prob. 17AYUCh. 11.3 - Prob. 18AYUCh. 11.3 - Prob. 19AYUCh. 11.3 - Prob. 20AYUCh. 11.3 - Prob. 21AYUCh. 11.3 - Prob. 22AYUCh. 11.3 - Putting It Together: Online Homework Professor...Ch. 11.3 - Prob. 24AYUCh. 11.3 - College Skills The Collegiate Learning Assessment...Ch. 11.3 - MythBusters In a MythBusters episode, the question...Ch. 11.3 - Prob. 27AYUCh. 11.4 - Prob. 1AYUCh. 11.4 - Prob. 2AYUCh. 11.4 - Prob. 3AYUCh. 11.4 - Prob. 4AYUCh. 11.4 - Prob. 5AYUCh. 11.4 - The following data represent the measure of a...Ch. 11.4 - Prob. 7AYUCh. 11.4 - TIMS Report and Kumon TIMS is an acronym for the...Ch. 11.4 - Age Difference in Married Couples What is the...Ch. 11.4 - Prob. 10AYUCh. 11.4 - Prob. 11AYUCh. 11.4 - Prob. 12AYUCh. 11.4 - Prob. 13AYUCh. 11.4 - Prob. 14AYUCh. 11.4 - Prob. 15AYUCh. 11.4 - Extramarital Affairs Is there a difference in the...Ch. 11.4 - Multitasking in School In todays wired society,...Ch. 11.4 - Prob. 18AYUCh. 11.4 - Hospital Readmission As of October 1, 2012,...Ch. 11.4 - Behavior and Gender at Work Researchers wanted to...Ch. 11.4 - Prob. 21AYUCh. 11.4 - Prob. 22AYUCh. 11.4 - Prob. 23AYUCh. 11.4 - Prob. 24AYUCh. 11.4 - Prob. 25AYUCh. 11.4 - Prob. 26AYUCh. 11.4 - Prob. 27AYUCh. 11.4 - In Problems 2231, for each study, explain which...Ch. 11.4 - Prob. 29AYUCh. 11.4 - Prob. 30AYUCh. 11.4 - In Problems 2231, for each study, explain which...Ch. 11 - In Problems 1 and 2, determine if the sampling is...Ch. 11 - In Problems 1 and 2, determine if the sampling is...Ch. 11 - In Problem 3, assume that the paired differences...Ch. 11 - In Problems 4 and 5, assume that the populations...Ch. 11 - In Problems 4 and 5, assume that the populations...Ch. 11 - A random sample of n1 = 555 individuals results in...Ch. 11 - Height versus Arm Span A statistics student heard...Ch. 11 - McDonalds versus Wendys A student wanted to...Ch. 11 - Treatment for Osteoporosis Osteoporosis is a...Ch. 11 - Determining Sample Size A nutritionist wants to...Ch. 11 - Height versus Arm Span Construct and interpret a...Ch. 11 - Prob. 12RECh. 11 - Prob. 1CTCh. 11 - Prob. 2CTCh. 11 - Prob. 3CTCh. 11 - Prob. 4CTCh. 11 - Prob. 5CTCh. 11 - Prob. 6CTCh. 11 - Prob. 7CTCh. 11 - In a study conducted to determine the role that...Ch. 11 - Researchers had a car traveling 10 miles per hour...Ch. 11 - Zoloft is a drug used to treat...Ch. 11 - Does hypnotism result in a different success rate...Ch. 11 - A researcher wants to estimate the difference...Ch. 11 - It is commonplace to gain weight after quitting...Ch. 11 - Dr. Penelope Nicholls is interested in exploring a...Ch. 11 - Dr. Penelope Nicholls is interested in exploring a...
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