 Chapter 12.1: Determine whether each situation would produce a random sample. Wri...
 Chapter 12.2: Determine whether each situation would produce a random sample. Wri...
 Chapter 12.3: For Exercises 35, find the margin of sampling error to the nearest ...
 Chapter 12.4: For Exercises 35, find the margin of sampling error to the nearest ...
 Chapter 12.5: For Exercises 35, find the margin of sampling error to the nearest ...
 Chapter 12.6: What does the 3% indicate about the results?
 Chapter 12.7: What does the 3% indicate about the results?
 Chapter 12.8: Determine whether each situation would produce a random sample. Wri...
 Chapter 12.9: Determine whether each situation would produce a random sample. Wri...
 Chapter 12.10: Determine whether each situation would produce a random sample. Wri...
 Chapter 12.11: Determine whether each situation would produce a random sample. Wri...
 Chapter 12.12: For Exercises 1221, find the margin of sampling error to the neares...
 Chapter 12.13: For Exercises 1221, find the margin of sampling error to the neares...
 Chapter 12.14: For Exercises 1221, find the margin of sampling error to the neares...
 Chapter 12.15: For Exercises 1221, find the margin of sampling error to the neares...
 Chapter 12.16: For Exercises 1221, find the margin of sampling error to the neares...
 Chapter 12.17: For Exercises 1221, find the margin of sampling error to the neares...
 Chapter 12.18: A poll asked people to name the most serious problem facing the cou...
 Chapter 12.19: In a recent survey, 431 fulltime employees were asked if the Inter...
 Chapter 12.20: Three hundred sixtyseven of 425 high school students said pizza wa...
 Chapter 12.21: Nine hundred thirtyfour of 2150 subscribers to a particular newspa...
 Chapter 12.22: According to a recent poll, 33% of shoppers planned to spend $1000 ...
 Chapter 12.23: One hundred people were asked whether they would vote for Candidate...
 Chapter 12.24: In a recent poll, 83% of the 1020 people surveyed said they support...
 Chapter 12.25: In a recent poll, 61% of the 1010 people surveyed said they conside...
 Chapter 12.26: Give examples of a biased sample and an unbiased sample. Explain yo...
 Chapter 12.27: Explain what happens to the margin of sampling error when the size ...
 Chapter 12.28: Use the information on page 742 to explain how surveys are used in ...
 Chapter 12.29: Use the information on page 742 to explain how surveys are used in ...
 Chapter 12.30: If x y 2 + y 1 = y 2 , then the value of x cannot equal which of...
 Chapter 12.31: A student guesses at all 5 questions on a truefalse quiz. Find eac...
 Chapter 12.32: A student guesses at all 5 questions on a truefalse quiz. Find eac...
 Chapter 12.33: A student guesses at all 5 questions on a truefalse quiz. Find eac...
 Chapter 12.34: What percent of the data lies between 39 and 61?
 Chapter 12.35: What is the probability that a data value selected at random is gre...
 Chapter 12.36: According to a poll of 300 people, 39% said that they favor Mrs. Sm...
 Chapter 12.37: In a poll asking people to name their most valued freedom, 51% of t...
 Chapter 12.38: According to a recent survey of mothers with children who play spor...
Solutions for Chapter Chapter 12: Sampling and Error
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter Chapter 12: Sampling and Error
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter Chapter 12: Sampling and Error includes 38 full stepbystep solutions. Since 38 problems in chapter Chapter 12: Sampling and Error have been answered, more than 42664 students have viewed full stepbystep solutions from this chapter. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Iterative method.
A sequence of steps intended to approach the desired solution.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).