 14.1: As part of a sixthgrade class project the teacher brings to class ...
 14.2: As part of a sixthgrade class project the teacher brings to class ...
 14.3: Madison County has a population of 34,522 people. The county hospit...
 14.4: Madison County has a population of 34,522 people. The county hospit...
 14.5: A big concert was held at the Bowl. Men and women had to go through...
 14.6: A large jar contains an unknown number of red gumballs and 150 gree...
 14.7: You want to estimate how many fish there are in a small pond. Lets ...
 14.8: To estimate the population in a rookery, 4965 fur seal pups were ca...
 14.9: To count whale populations, the capture is done by means of a photo...
 14.10: The critically endangered Mauis dolphin is currently restricted to ...
 14.11: Exercises 11 and 12 refer to Chapmans correction. Chapmans correcti...
 14.12: Exercises 11 and 12 refer to Chapmans correction. Chapmans correcti...
 14.13: Starting in 2004, a study to determine the number of lake sturgeon ...
 14.14: A 2004 study conducted at Utah Lake using the capturerecapture meth...
 14.15: Name the sampling method that best describes each situation. Choose...
 14.16: An audit is performed on last years 15,000 studentaid packages giv...
 14.17: Exercises 17 through 20 refer to the following story: The city of C...
 14.18: Exercises 17 through 20 refer to the following story: The city of C...
 14.19: Exercises 17 through 20 refer to the following story: The city of C...
 14.20: Exercises 17 through 20 refer to the following story: The city of C...
 14.21: Exercises 21 through 24 refer to the following story: The 1250 stud...
 14.22: Exercises 21 through 24 refer to the following story: The 1250 stud...
 14.23: Exercises 21 through 24 refer to the following story: The 1250 stud...
 14.24: Exercises 21 through 24 refer to the following story: The 1250 stud...
 14.25: Exercises 25 through 28 refer to the following story: The Cleansbur...
 14.26: Exercises 25 through 28 refer to the following story: The Cleansbur...
 14.27: Exercises 25 through 28 refer to the following story: The Cleansbur...
 14.28: Exercises 25 through 28 refer to the following story: The Cleansbur...
 14.29: Exercises 29 through 32 refer to the following story: The dean of s...
 14.30: Exercises 29 through 32 refer to the following story: The dean of s...
 14.31: Exercises 29 through 32 refer to the following story: The dean of s...
 14.32: Exercises 29 through 32 refer to the following story: The dean of s...
 14.33: Exercises 33 and 34 refer to the following story: An orange grower ...
 14.34: Exercises 33 and 34 refer to the following story: An orange grower ...
 14.35: You are a fruit wholesaler. You have just received 250 crates of pi...
 14.36: For each of the following situations, determine if the sample is re...
 14.37: Exercises 37 through 40 refer to the following story: The manufactu...
 14.38: Exercises 37 through 40 refer to the following story: The manufactu...
 14.39: Exercises 37 through 40 refer to the following story: The manufactu...
 14.40: Exercises 37 through 40 refer to the following story: The manufactu...
 14.41: Exercises 41 through 44 refer to a clinical study conducted at the ...
 14.42: Exercises 41 through 44 refer to a clinical study conducted at the ...
 14.43: Exercises 41 through 44 refer to a clinical study conducted at the ...
 14.44: Exercises 41 through 44 refer to a clinical study conducted at the ...
 14.45: Exercises 45 through 48 refer to a clinical trial named APPROVe des...
 14.46: Exercises 45 through 48 refer to a clinical trial named APPROVe des...
 14.47: Exercises 45 through 48 refer to a clinical trial named APPROVe des...
 14.48: Exercises 45 through 48 refer to a clinical trial named APPROVe des...
 14.49: Exercises 49 through 52 refer to a study on the effectiveness of an...
 14.50: Exercises 49 through 52 refer to a study on the effectiveness of an...
 14.51: Exercises 49 through 52 refer to a study on the effectiveness of an...
 14.52: Exercises 49 through 52 refer to a study on the effectiveness of an...
 14.53: Exercises 53 through 56 refer to a landmark study conducted in 1896...
 14.54: Exercises 53 through 56 refer to a landmark study conducted in 1896...
 14.55: Exercises 53 through 56 refer to a landmark study conducted in 1896...
 14.56: Exercises 53 through 56 refer to a landmark study conducted in 1896...
 14.57: Exercises 57 through 60 refer to a study conducted between 2008 and...
 14.58: Exercises 57 through 60 refer to a study conducted between 2008 and...
 14.59: Exercises 57 through 60 refer to a study conducted between 2008 and...
 14.60: Exercises 57 through 60 refer to a study conducted between 2008 and...
 14.61: Imagine you have a very large coin jar full of nickels, dimes, and ...
 14.62: One implicit assumption when using the capturerecapture method to ...
 14.63: One implicit assumption when using the capturerecapture method to ...
 14.64: Informal surveys. In everyday life we are constantly involved in ac...
 14.65: Read the examples of informal surveys given in Exercise 64. Give th...
 14.66: Leadingquestion bias. The way the questions in many surveys are ph...
 14.67: Question order bias. In July 1999, a Gallup poll of 1061 people ask...
 14.68: Today, most consumer marketing surveys are conducted by telephone. ...
 14.69: The following two surveys were conducted in January 1991 to assess ...
 14.70: An article in the Providence Journal about automobile accident fata...
 14.71: a) For the capturerecapture method to give a reasonable estimate o...
 14.72: Consider the following hypothetical survey designed to find out wha...
 14.73: One of the problems with the capturerecapture method is that in so...
 14.74: Darrochs method. is a method for estimating the size of a populatio...
Solutions for Chapter 14: Censuses, Surveys, Polls, and Studies
Full solutions for Excursions in Modern Mathematics  8th Edition
ISBN: 9781292022048
Solutions for Chapter 14: Censuses, Surveys, Polls, and Studies
Get Full SolutionsExcursions in Modern Mathematics was written by and is associated to the ISBN: 9781292022048. Chapter 14: Censuses, Surveys, Polls, and Studies includes 74 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Excursions in Modern Mathematics, edition: 8. Since 74 problems in chapter 14: Censuses, Surveys, Polls, and Studies have been answered, more than 11894 students have viewed full stepbystep solutions from this chapter.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Solvable system Ax = b.
The right side b is in the column space of A.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.