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# Solutions for Chapter 4.1: Sample Spaces and Probability

## Full solutions for Elementary Statistics: A Step By Step Approach | 9th Edition

ISBN: 9780073534985

Solutions for Chapter 4.1: Sample Spaces and Probability

Solutions for Chapter 4.1
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##### ISBN: 9780073534985

Summary of Chapter 4.1: Sample Spaces and Probability

A sample space is the set of all possible outcomes of a probability experiment.

This textbook survival guide was created for the textbook: Elementary Statistics: A Step By Step Approach , edition: 9. Elementary Statistics: A Step By Step Approach was written by and is associated to the ISBN: 9780073534985. Chapter 4.1: Sample Spaces and Probability includes 33 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 33 problems in chapter 4.1: Sample Spaces and Probability have been answered, more than 666780 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• -error (or -risk)

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

• Analytic study

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

• Average

See Arithmetic mean.

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Bivariate distribution

The joint probability distribution of two random variables.

• Categorical data

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

• Central limit theorem

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• Conditional mean

The mean of the conditional probability distribution of a random variable.

• Conditional probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• Conidence level

Another term for the conidence coeficient.

• Counting techniques

Formulas used to determine the number of elements in sample spaces and events.

• Critical region

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

• Defects-per-unit control chart

See U chart

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• False alarm

A signal from a control chart when no assignable causes are present

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

• Gaussian distribution

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

• Geometric mean.

The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.