Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 11.5, Problem 1P
Using (5.3) with (3.4) and
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Students have asked these similar questions
(a) Test the hypothesis.
Consider the hypothesis test Ho
=
:
against H₁o < 02. Suppose that the sample sizes aren₁ =
7 and n₂
= 13 and that
$²
= 22.4 and $22
= 28.2. Use α = 0.05.
Ho
is not
✓ rejected.
9-9
IV
(b) Find a 95% confidence interval on of 102. Round your answer to two decimal places (e.g. 98.76).
Let us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a
university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when
examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both
sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force
for using ultrasound was 6.4 pounds with standard deviation 0.3 pounds. Assume that the standard deviations are known.
Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null
hypothesis, 40 = 0. What level of type II error would you recommend here?
Round your answer to four decimal places (e.g. 98.7654). Use a
= 0.05.
β
= i
What sample size would be required?
Assume the sample sizes are to be equal.…
=
Consider the hypothesis test Ho: μ₁ = μ₂ against H₁ μ₁ μ2. Suppose that sample sizes are n₁ =
15 and n₂ =
15, that x1 = 4.7
and X2 = 7.8 and that s² = 4 and s² = 6.26. Assume that o and that the data are drawn from normal distributions. Use
απ 0.05.
(a) Test the hypothesis and find the P-value.
(b) What is the power of the test in part (a) for a true difference in means of 3?
(c) Assuming equal sample sizes, what sample size should be used to obtain ẞ = 0.05 if the true difference in means is - 2? Assume
that α = 0.05.
(a) The null hypothesis is
98.7654).
rejected. The P-value is 0.0008
(b) The power is 0.94
. Round your answer to four decimal places (e.g.
Round your answer to two decimal places (e.g. 98.76).
(c) n₁ = n2 =
1
. Round your answer to the nearest integer.
Chapter 11 Solutions
Mathematical Methods in the Physical Sciences
Ch. 11.3 - The integral in ( 3.1) is improper because of the...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a T...Ch. 11.3 - Express each of the following integrals as a ...
Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - A particle starting from rest at x=1 moves along...Ch. 11.3 - Express as a function 01ln1xp1dx, Hint: See...Ch. 11.5 - Using (5.3) with (3.4) and (4.1), find...Ch. 11.5 - Without computer or tables, but just using facts...Ch. 11.5 - In Chapter 1, equations(13.5)and (13.6), we...Ch. 11.5 - Prove that, for positive integral n:...Ch. 11.5 - Use (5.4) to show that (a) 12n12+n=(1)n if n= a...Ch. 11.5 - Prove...Ch. 11.5 - In the Table of Laplace Transforms (end of Chapter...Ch. 11.6 - Prove that B(p,q)=B(q,p). Hint: Put x=1y in...Ch. 11.6 - Prove equation (6.5) (6.5)B(p,q)=0yp1dy(1+y)p+q.Ch. 11.6 - Show that for integral n, m...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Prove B(n,n)=Bn,12/22n1. Hint: In (6.4), use the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.8 - Complete the pendulum problem to find the period...Ch. 11.8 - Suppose that a car with a door open at right...Ch. 11.8 - The figure is part of a cycloid with parametric...Ch. 11.9 - Sketch or computer plot a graph of the function...Ch. 11.9 - Verify equations (9.2),(9.3), and (9.4). Hint:...Ch. 11.9 - Prove that erf(x) is an odd function of x. Hint:...Ch. 11.9 - Show that ey2/2dy=2 (a) by using (9.5) and (9.2a);...Ch. 11.9 - Replace x by $i x in(9.1)andlet t = i u$ to show...Ch. 11.9 - Assuming that x is real, show the following...Ch. 11.10 - Carry through the algebra to get equation (10.4).Ch. 11.10 - The integral xtp1etdt=(p,x) is called an...Ch. 11.10 - Express the complementary error function erfc (x)...Ch. 11.10 - En(x)=1exttndt,n=0,1,2,, and Ei(x)=xettdt, and...Ch. 11.10 - 2(a) Express E1(x) as an incomplete function. (b)...Ch. 11.10 - The logarithmic integral is li(x)=0xdtlnt. Express...Ch. 11.10 - Computer plot graphs of (a) En(x) for n=0 to 10...Ch. 11.11 - Use the term 1/(12p) in (11.5) to show that the...Ch. 11.11 - (a) To see the results in Problem 1 graphically,...Ch. 11.11 - In statistical mechanics, we frequently use the...Ch. 11.11 - Use Stirlings formula to evaluate...Ch. 11.11 - Use Stirlings formula to evaluate limnn+32n(n+1).Ch. 11.11 - Use equations (3.4) and (11.5) to show that...Ch. 11.11 - The function (p)=ddpln(p) is called the digamma...Ch. 11.11 - Sketch or computer plot a graph of y=lnx for x0....Ch. 11.11 - The following expression occurs in statistical...Ch. 11.11 - Use Stirlings formula to find limn(n!)1/n/n.Ch. 11.12 - Expand the integrands of K and E [see ( 12.3 )] in...Ch. 11.12 - Use a graph of sin2 and the text discussion just...Ch. 11.12 - Computer plot graphs of K(k) and E(k) in (12.3)...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - Find the circumference of the ellipse 4x2+9y2=36.Ch. 11.12 - Find the length of arc of the ellipse x2+y2/4=1...Ch. 11.12 - Find the are length of one arch of y=sinx.Ch. 11.12 - Write the integral in equation (12.7) as an...Ch. 11.12 - Computer plot graphs of sn u, cn u, and dn u, for...Ch. 11.12 - If u=ln(sec+tan), then is a function of u called...Ch. 11.12 - Show that for k=0:u=F(,0)=,snu=sinu,cnu=cosu,dnu=1...Ch. 11.12 - Show that the four answers given in Section 1 for...Ch. 11.12 - In the pendulum problem, =sing/lt is an...Ch. 11.12 - A uniform solid sphere of density 12 is floating...Ch. 11.12 - Sometimes you may find the notation F(,k) in...Ch. 11.12 - As in Problem $24,$ show that...Ch. 11.13 - Show that $ 0ymdy(1+y)n+1=1(nm)C(n,m) $ for...Ch. 11.13 - Show that B(m,n)B(m+n,k)=B(n,k)B(n+k,m).Ch. 11.13 - Use Stirlings formula to show that...Ch. 11.13 - Verify the asymptotic series 0etdt(1+xt)~ (1)nn!xn...Ch. 11.13 - Use gamma and beta function formulas to show that...Ch. 11.13 - Generalize Problem 5 to show that...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Find an expression for the exact value of (55.5)...Ch. 11.13 - Using your result in Problem 23 and equation...Ch. 11.13 - As in problems 23 and 24, find expressions for the...
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