MyLab Statistics with Pearson eText -- Standalone Access Card -- for Elementary Statistics Using Excel (My Stat Lab)
6th Edition
ISBN: 9780134748849
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 10, Problem 1CQQ
To determine
To conclude: About the linear correlationbetween the numbers of enrolled students and numbers of burglaries.
Expert Solution & Answer
Answer to Problem 1CQQ
There is no sufficient evidence to support the claim that there is a
Explanation of Solution
Given info:
The data shows that the numbers of enrolled students (in thousands) and the numbers of burglaries. The
Calculation:
The hypotheses are given below:
Null hypothesis:
That is, there is no linear correlation betweenthe numbers of enrolled students and the numbers of burglaries.
Alternative hypothesis:
That is, there is a linear correlation between the numbers of enrolled students and the numbers of burglaries.
Conclusion:
The P-value is 0.393 and the level of significance is 0.05.
Here, the P-value is greater than the level of significance.
Hence, the null hypothesis isnot rejected. That is, there is no linear correlation betweenthe numbers of enrolled students and the numbers of burglaries.
The critical value is ±0.878.
Here, the correlation value is 0.499 which lies between the critical values.
Hence, the null hypothesis isnot rejected.
Thus, there is nosufficient evidence to support the claim that there is a linear correlation betweenthe numbers of enrolled students and the numbers of burglaries.
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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 10 Solutions
MyLab Statistics with Pearson eText -- Standalone Access Card -- for Elementary Statistics Using Excel (My Stat Lab)
Ch. 10.1 - 1. Notation Twenty different statistics students...Ch. 10.1 - Prob. 2BSCCh. 10.1 - 3. Global Warming If we find that there is a...Ch. 10.1 - 4. Scatterplots Match these values of r with the...Ch. 10.1 - 5. Bear Weight and Chest Size Fifty-four wild...Ch. 10.1 - Prob. 6BSCCh. 10.1 - Prob. 7BSCCh. 10.1 - Prob. 8BSCCh. 10.1 - Explore! Exercises 9 and 10 provide two data sets...Ch. 10.1 - Prob. 10BSC
Ch. 10.1 - Prob. 11BSCCh. 10.1 - Prob. 12BSCCh. 10.1 - Prob. 13BSCCh. 10.1 - Prob. 14BSCCh. 10.1 - Testing for a Linear Correlation. In Exercises...Ch. 10.1 - Prob. 16BSCCh. 10.1 - Prob. 17BSCCh. 10.1 - Prob. 18BSCCh. 10.1 - Prob. 19BSCCh. 10.1 - Prob. 20BSCCh. 10.1 - Prob. 21BSCCh. 10.1 - Testing for a Linear Correlation. In Exercises...Ch. 10.1 - Prob. 23BSCCh. 10.1 - Prob. 24BSCCh. 10.1 - Testing for a Linear Correlation. In Exercises...Ch. 10.1 - Prob. 26BSCCh. 10.1 - Prob. 27BSCCh. 10.1 - Prob. 28BSCCh. 10.1 - Prob. 29BSCCh. 10.1 - Prob. 30BSCCh. 10.1 - Prob. 31BSCCh. 10.1 - Prob. 32BSCCh. 10.1 - Prob. 33BSCCh. 10.1 - Prob. 34BSCCh. 10.1 - Prob. 35BBCh. 10.1 - Prob. 36BBCh. 10.2 - Prob. 1BSCCh. 10.2 - Prob. 2BSCCh. 10.2 - Prob. 3BSCCh. 10.2 - 4. Correlation and Slope What is the relationship...Ch. 10.2 - Prob. 5BSCCh. 10.2 - Prob. 6BSCCh. 10.2 - Making Predictions. In Exercises 5–8, let the...Ch. 10.2 - Making Predictions. In Exercises 5–8, let the...Ch. 10.2 - Finding the Equation of the Regression Line. In...Ch. 10.2 - Prob. 10BSCCh. 10.2 - Prob. 11BSCCh. 10.2 - Prob. 12BSCCh. 10.2 - Regression and Predictions. Exercises 13–28 use...Ch. 10.2 - Prob. 14BSCCh. 10.2 - Prob. 15BSCCh. 10.2 - Prob. 16BSCCh. 10.2 - Prob. 17BSCCh. 10.2 - Prob. 18BSCCh. 10.2 - Prob. 19BSCCh. 10.2 - Regression and Predictions. Exercises 13–28 use...Ch. 10.2 - Prob. 21BSCCh. 10.2 - Prob. 22BSCCh. 10.2 - Regression and Predictions. Exercises 13–28 use...Ch. 10.2 - Prob. 24BSCCh. 10.2 - Prob. 25BSCCh. 10.2 - Prob. 26BSCCh. 10.2 - Prob. 27BSCCh. 10.2 - Prob. 28BSCCh. 10.2 - Prob. 29BSCCh. 10.2 - Prob. 30BSCCh. 10.2 - Prob. 31BSCCh. 10.2 - Prob. 32BSCCh. 10.2 - Prob. 33BSCCh. 10.2 - Prob. 34BSCCh. 10.2 - Prob. 35BBCh. 10.3 - Prob. 1BSCCh. 10.3 - 2. Prediction Interval Using the heights and...Ch. 10.3 - Prob. 3BSCCh. 10.3 - Prob. 4BSCCh. 10.3 - Prob. 5BSCCh. 10.3 - Prob. 6BSCCh. 10.3 - Prob. 7BSCCh. 10.3 - Prob. 8BSCCh. 10.3 - Prob. 9BSCCh. 10.3 - Prob. 10BSCCh. 10.3 - Prob. 11BSCCh. 10.3 - Prob. 12BSCCh. 10.3 - Prob. 13BSCCh. 10.3 - Prob. 14BSCCh. 10.3 - Prob. 15BSCCh. 10.3 - Prob. 16BSCCh. 10.3 - Prob. 17BSCCh. 10.3 - Prob. 18BSCCh. 10.3 - Prob. 19BSCCh. 10.3 - Prob. 20BSCCh. 10.3 - Prob. 21BBCh. 10.4 - Prob. 1BSCCh. 10.4 - 2. Best Multiple Regression Equation For the...Ch. 10.4 - Prob. 3BSCCh. 10.4 - 4. Interpreting R2 For the multiple regression...Ch. 10.4 - Prob. 5BSCCh. 10.4 - Prob. 6BSCCh. 10.4 - Prob. 7BSCCh. 10.4 - Prob. 8BSCCh. 10.4 - Prob. 9BSCCh. 10.4 - Prob. 10BSCCh. 10.4 - Prob. 11BSCCh. 10.4 - Prob. 12BSCCh. 10.4 - Prob. 13BSCCh. 10.4 - Prob. 14BSCCh. 10.4 - Appendix B Data Sets. In Exercises 13 – 16, refer...Ch. 10.4 - Prob. 16BSCCh. 10.4 - Prob. 17BBCh. 10.4 - Prob. 18BBCh. 10.4 - Prob. 19BBCh. 10.5 - 1. Identifying a Model and R2 Different samples...Ch. 10.5 - Prob. 2BSCCh. 10.5 - Prob. 3BSCCh. 10.5 - Prob. 4BSCCh. 10.5 - Prob. 5BSCCh. 10.5 - Prob. 6BSCCh. 10.5 - Prob. 7BSCCh. 10.5 - Prob. 8BSCCh. 10.5 - Prob. 9BSCCh. 10.5 - Finding the Best Model. In Exercises 5–16,...Ch. 10.5 - Prob. 11BSCCh. 10.5 - Prob. 12BSCCh. 10.5 - Prob. 13BSCCh. 10.5 - Prob. 14BSCCh. 10.5 - Prob. 15BSCCh. 10.5 - Prob. 16BSCCh. 10.5 - Prob. 17BBCh. 10.5 - Prob. 18BBCh. 10 - Prob. 1CQQCh. 10 - Prob. 2CQQCh. 10 - Prob. 3CQQCh. 10 - Prob. 4CQQCh. 10 - Prob. 5CQQCh. 10 - Prob. 6CQQCh. 10 - Prob. 7CQQCh. 10 - Prob. 8CQQCh. 10 - Prob. 9CQQCh. 10 - Prob. 10CQQCh. 10 - Prob. 1RECh. 10 - Cigarette Nicotine and Carbon Monoxide Refer to...Ch. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 1CRECh. 10 - Prob. 2CRECh. 10 - Prob. 3CRECh. 10 - Prob. 4CRECh. 10 - Prob. 5CRECh. 10 - Prob. 6CRECh. 10 - Prob. 7CRECh. 10 - Prob. 8CRECh. 10 - Prob. 1EPCh. 10 - Prob. 2EPCh. 10 - Prob. 3EPCh. 10 - Prob. 4EPCh. 10 - Prob. 5EPCh. 10 - Prob. 6EPCh. 10 - Prob. 1FDDCh. 10 - Prob. 2FDDCh. 10 - Prob. 3FDDCh. 10 - Prob. 4FDDCh. 10 - Prob. 5FDD
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