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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Textbook Question
Chapter 2.8, Problem 18E
In the descriptions of experiments given in Exercises 2.15–2.18, identify the important features of each design. Include as many of the components listed in Exercise 2.14 as needed to adequately describe the design.
2.18 Researchers in an education department at a large state university have designed a study to compare the math abilities of students in junior high. They will also examine the impact of three types of schools — public, private nonparochial, and parochial — on the scores the students receive in a standardized math test. Two large cities in each of four geographical regions of the United States were selected for the study. In each city, one school of each of the three types was randomly selected, and a single eighth-grade class was randomly selected within each school.
The scores on the test were recorded for each student in the selected classrooms. The researcher was concerned about differences in socio-economie status among the 8 cities, so she obtained a measure of socioeconomic status for each of the students that participated in the study.
2.14 The process engineer designed a study to evaluate the quality of plastic irrigation pipes. The study involved a total of 48 pipes; 24 pipes were randomly selected from each of the company’s two manufacturing plants. The pipes were heat-treated at one one of four temperatures (175, 200, 225, 250°F). The pipes were chemically treated with one of three types of hardeners (H1, H2, H3). The deviations from the nominal compressive strength were measured at five locations on each of the pipes.
Identify each of the following components of the experimental design.
- a. Factors
- b. Factor levels
- c. Blocks
- d. Experimental unit
- e. Measurement unit
- f. Replications
- g.
Covariates - h. Treatments
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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 2 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 2.8 - In the following descriptions of a study,...Ch. 2.8 - In the following descriptions of a study,...Ch. 2.8 - A news report states that minority children who...Ch. 2.8 - A study was conducted to determine if the...Ch. 2.8 - Prob. 5ECh. 2.8 - A large auto parts supplier with distribution...Ch. 2.8 - The circuit judges in a rural county are...Ch. 2.8 - Prob. 8ECh. 2.8 - Time magazine, in an article in the late 1950s,...Ch. 2.8 - The New York City school district is planning a...
Ch. 2.8 - A professional society, with a membership of...Ch. 2.8 - For each of the following situations, decide what...Ch. 2.8 - For each of the following situations, decide what...Ch. 2.8 - The process engineer designed a study to evaluate...Ch. 2.8 - Prob. 15ECh. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - A research specialist for a large seafood company...Ch. 2.8 - In Exercises 2.20–2.22, identify whether the...Ch. 2.8 - In Exercises 2.202.22, identify whether the design...Ch. 2.8 - In Exercises 2.20–2.22, identify whether the...Ch. 2.8 - A bakery wants to evaluate new recipes for carrot...Ch. 2.8 - Prob. 24SECh. 2.8 - Prob. 25SECh. 2.8 - Prob. 26SECh. 2.8 - Prob. 27SECh. 2.8 - Prob. 28SECh. 2.8 - Prob. 29SECh. 2.8 - A forester wants to estimate the total number of...Ch. 2.8 - A transportation researcher is funded to estimate...Ch. 2.8 - The department of agriculture in a midwestern...Ch. 2.8 - Prob. 33SECh. 2.8 - A Yankelovich, Skelly, and White poll taken in the...
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