Essentials of Statistics (6th Edition)
6th Edition
ISBN: 9780134685779
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 7.3, Problem 21BSC
Determining
21. Statistics Student Incomes You want to estimate the standard deviation of the annual incomes of all current statistics students. Find the minimum sample size needed to be 95% confident that the sample standard deviation is within 20% of the population standard deviation. Are those incomes likely to satisfy the requirement of a normal distribution?
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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 7 Solutions
Essentials of Statistics (6th Edition)
Ch. 7.1 - Poll Results in the Media USA Today provided...Ch. 7.1 - Margin of Error For the poll described in Exercise...Ch. 7.1 - Notation For the poll described in Exercise 1,...Ch. 7.1 - Confidence Levels Given specific sample data, such...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...
Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Touch Therapy When she was 9 years of age, Emily...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Finite Population Correction Factor For Formulas...Ch. 7.1 - One-Sided Confidence Interval A one-sided claim...Ch. 7.1 - Coping with No Success According to the Rule of...Ch. 7.2 - In Exercises 13, refer to the accompanying screen...Ch. 7.2 - Statistical Literacy and Critical Thinking In...Ch. 7.2 - In Exercises 13, refer to the accompanying screen...Ch. 7.2 - Normality Requirement What does it mean when we...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Confidence Interval with Known . In Exercises 37...Ch. 7.2 - Confidence Interval with Known . In Exercises 37...Ch. 7.2 - Finite Population Correction Factor If a simple...Ch. 7.3 - Brain Volume Using all of the brain volumes listed...Ch. 7.3 - Expressing Confidence Intervals Example 2 showed...Ch. 7.3 - Last Digit Analysis The dotplot below depicts the...Ch. 7.3 - Normality Requirement What is different about the...Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Comparing Waiting Lines a. The values listed below...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Finding Critical Values In constructing confidence...Ch. 7.3 - Finding Sample Size Instead of using Table 7-2 for...Ch. 7.4 - Replacement Why does the bootstrap method require...Ch. 7.4 - Bootstrap Sample Here is a random sample of...Ch. 7.4 - Bootstrap Sample Given the sample data from...Ch. 7.4 - Prob. 4BSCCh. 7.4 - In Exercises 58, use the relatively small number...Ch. 7.4 - In Exercises 58, use the relatively small number...Ch. 7.4 - In Exercises 58, use the relatively small number...Ch. 7.4 - In Exercises 58, use the relatively small number...Ch. 7 - Celebrities and the Law Here is a 95% confidence...Ch. 7 - Interpreting CI Write a brief statement that...Ch. 7 - Critical Value For the survey described in...Ch. 7 - Loose Change USA Today reported that 40% of people...Ch. 7 - Sample Size for Proportion Find the sample size...Ch. 7 - Sample Size for Mean Find the sample size required...Ch. 7 - Requirements A quality control analyst has...Ch. 7 - Degrees of Freedom In general, what does degrees...Ch. 7 - Critical Value Refer to Exercise 7 Requirements...Ch. 7 - Which Method? Refer to Exercise 7 Requirements and...Ch. 7 - Online News In a Harris poll of 2036 adults, 40%...Ch. 7 - Computers In order to better plan for student...Ch. 7 - Earthquake Magnitudes Listed below are Richter...Ch. 7 - Lefties There have been several studies conducted...Ch. 7 - Distributions Identify the distribution (normal,...Ch. 7 - Sample Size You have been hired by your new...Ch. 7 - Wristwatch Accuracy Students of the author...Ch. 7 - Wristwatch Accuracy Use the sample data from...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Normal Distribution Using a larger data set than...Ch. 7 - Sample Size Find the sample size necessary to...Ch. 7 - Prob. 7CRECh. 7 - Normality Assessment A random sample consists of...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...
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