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# Solutions for Chapter Chapter 23: Two Categorical Variables: The Chi-Square Test

## Full solutions for The Basic Practice of Statistics | 4th Edition

ISBN: 9780716774785

Solutions for Chapter Chapter 23: Two Categorical Variables: The Chi-Square Test

Solutions for Chapter Chapter 23
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##### ISBN: 9780716774785

This textbook survival guide was created for the textbook: The Basic Practice of Statistics, edition: 4. Since 48 problems in chapter Chapter 23: Two Categorical Variables: The Chi-Square Test have been answered, more than 13531 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter Chapter 23: Two Categorical Variables: The Chi-Square Test includes 48 full step-by-step solutions. The Basic Practice of Statistics was written by and is associated to the ISBN: 9780716774785.

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

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

• Attribute control chart

Any control chart for a discrete random variable. See Variables control chart.

• Bernoulli trials

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

• Biased estimator

Unbiased estimator.

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• Central tendency

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

• Comparative experiment

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

• Conditional probability mass function

The probability mass function of the conditional probability distribution of a discrete random variable.

• Continuous uniform random variable

A continuous random variable with range of a inite interval and a constant probability density function.

• Control chart

A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• Cumulative sum control chart (CUSUM)

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

• Dependent variable

The response variable in regression or a designed experiment.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Experiment

A series of tests in which changes are made to the system under study

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• False alarm

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

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

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