An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Chapter 5.12, Problem 36E
The ability to read rapidly and simultaneously maintain a high level of comprehension is often a determining factor in the academic success of many high school students. A school district is considering a supplemental reading program for incoming freshmen. Prior to implementing the program, the school runs a pilot program on a random sample of n = 20 students. The students were thoroughly tested to determine reading speed and reading comprehension. Based on a fixed-length standardized test reading passage, the following reading times (in minutes) and comprehension scores (based on a 100-point scale) were recorded.
- a. What is the population about which inferences are being made?
- b. Place a 95% confidence interval on the
mean reading time for all incoming freshmen in the district. - c. Plot the reading time using a normal
probability plot or boxplot. Do the data appear to be a random sample from a population having anormal distribution ? - d. Provide an interpretation of the
interval estimate in part (b).
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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.)
Chapter 5 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 5.12 - The county government in a city that is dominated...Ch. 5.12 - In the research study on percentage of calories...Ch. 5.12 - Face masks used by firefighters often fail by...Ch. 5.12 - Refer to Exercise 5.3. Describe a process to...Ch. 5.12 - A company that manufacturers coffee for use in...Ch. 5.12 - Refer to Exercise 5.5. The engineer in charge of...Ch. 5.12 - Refer to Exercise 5.5. Because the company is...Ch. 5.12 - As part of the recruitment of new businesses, the...Ch. 5.12 - A program to reduce recidivism has been in effect...Ch. 5.12 - The susceptibility of the root stocks of a variety...
Ch. 5.12 - Prob. 11ECh. 5.12 - In any given situation, if the level of confidence...Ch. 5.12 - A biologist wishes to estimate the effect of an...Ch. 5.12 - Refer to Exercise 5.14. Suppose the mayors staff...Ch. 5.12 - Refer to Exercise 5.14. Suppose the mayors staff...Ch. 5.12 - A study is designed to test the hypotheses H0: ...Ch. 5.12 - Refer to Exercise 5.16. Graph the power curve for...Ch. 5.12 - A study was conducted of 90 adult male patients...Ch. 5.12 - Prob. 22ECh. 5.12 - A national agency sets recommended daily dietary...Ch. 5.12 - To evaluate the success of a 1-year experimental...Ch. 5.12 - Refer to Exercise 5.24. Suppose a random sample of...Ch. 5.12 - The administrator of a nursing home would like to...Ch. 5.12 - The vulnerability of inshore environments to...Ch. 5.12 - The RD department of a paint company has developed...Ch. 5.12 - Prob. 29ECh. 5.12 - A concern to public health officials is whether a...Ch. 5.12 - Prob. 31ECh. 5.12 - Prob. 32ECh. 5.12 - Prob. 33ECh. 5.12 - Provide the rejection region based on a t-test...Ch. 5.12 - A study was designed to evaluate whether the...Ch. 5.12 -
The ability to read rapidly and simultaneously...Ch. 5.12 - Refer to Exercise 5.36. Using the reading...Ch. 5.12 -
Refer to Exercise 5.36.
Does there appear to be a...Ch. 5.12 - A consumer testing agency wants to evaluate the...Ch. 5.12 -
Refer to Exercise 5.39.
Does the normality of the...Ch. 5.12 - The amount of sewage and industrial pollutants...Ch. 5.12 - A dealer in recycled paper places empty trailers...Ch. 5.12 - Prob. 47ECh. 5.12 - Prob. 48ECh. 5.12 - Prob. 49ECh. 5.12 - Prob. 50ECh. 5.12 - Prob. 51ECh. 5.12 - Prob. 52ECh. 5.12 - Prob. 53ECh. 5.12 - Prob. 54ECh. 5.12 - Prob. 55ECh. 5.12 - Prob. 56ECh. 5.12 - Prob. 57SECh. 5.12 - The concentration of mercury in a lake has been...Ch. 5.12 -
In a standard dissolution test for tablets of a...Ch. 5.12 - Prob. 60SECh. 5.12 -
Over the past 5 years, the mean time for a...Ch. 5.12 - If a new process for mining copper is to be put...Ch. 5.12 - Prob. 63SECh. 5.12 - Prob. 64SECh. 5.12 - Prob. 65SECh. 5.12 - Prob. 66SECh. 5.12 - Prob. 67SECh. 5.12 - Prob. 68SECh. 5.12 - Prob. 69SECh. 5.12 - Prob. 70SECh. 5.12 - Prob. 71SECh. 5.12 - Prob. 73SECh. 5.12 - Prob. 74SECh. 5.12 - Prob. 75SECh. 5.12 - Prob. 76SE
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