Essentials of Statistics for the Behavioral Sciences
8th Edition
ISBN: 9781133956570
Author: Frederick J Gravetter, Larry B. Wallnau
Publisher: Cengage Learning
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Textbook Question
Chapter 9.4, Problem 1LC
A new over-the-counter cold medication includes a warning label stating that it “may cause drowsiness.” A researcher would like to evaluate this effect. It is know n that under regular circumstances the distribution of reaction times is normal with
a. Use a two-tailed test with
b. Write a sentence that demonstrates how the outcome of the hypothesis test would appear in a research report.
c. Use a one-tailed lest with
d. Write a sentence that demonstrates how the outcome of the one-tailed hypothesis test would appear in a research report.
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Students have asked these similar questions
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?
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?
2
Chapter 9 Solutions
Essentials of Statistics for the Behavioral Sciences
Ch. 9.1 - Under what circumstances is a t statistic used...Ch. 9.1 - A sample of n = 9 scores has SS = 288. a. Compute...Ch. 9.1 - Prob. 3LCCh. 9.1 - Prob. 4LCCh. 9.1 - For df = 15, find the value(s) of t associated...Ch. 9.2 - A sample of n = 4 individuals is selected from a...Ch. 9.3 - If all other factors are held constant, an 80%...Ch. 9.3 - If all other factors are held constant, a...Ch. 9.3 - Prob. 1LCACh. 9.3 - How does sample size influence the outcome of a...
Ch. 9.4 - A new over-the-counter cold medication includes a...Ch. 9 - Under what circumstances is a t statistic used...Ch. 9 - A sample of n = 25 scores has a mean of M = 83 and...Ch. 9 - Find the estimated standard error for the sample...Ch. 9 - Explain why t distributions tend to be flatter and...Ch. 9 - Find the t values that form the boundaries of the...Ch. 9 - The following sample of n = 6 scores was obtained...Ch. 9 - The following sample was obtained from a...Ch. 9 - A random rumple of n = 25 individuals is selected...Ch. 9 - To evaluate the effect of a treatment, a sample is...Ch. 9 - To evaluate the effect of a treatment, a sample of...Ch. 9 - The spotlight effect refers to overestimating the...Ch. 9 - Many animals, including humans, tend to avoid...Ch. 9 - Standardized measures seem to indicate that the...Ch. 9 - The librarian at the local elementary school...Ch. 9 - For several years researchers have noticed that...Ch. 9 - Weinstein, McDermott, and Roediger (2010) report...Ch. 9 - Ackerman and Goldsmith (2011) found that students...Ch. 9 - A random sample of n = 16 scores is obtained from...Ch. 9 - A random sample is obtained from a population with...Ch. 9 - An example of the vertical-horizontal illusion is...Ch. 9 - McGee and Shevlin (2009) demonstrated that an...Ch. 9 - Oishi and Shigehiro (2010) report that people who...Ch. 9 - Prob. 23P
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