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# Solutions for Chapter 15.3: INFERENCES ABOUT MEASURES OF CENTRAL TENDENCY

## Full solutions for Statistics: Informed Decisions Using Data | 4th Edition

ISBN: 9780321757272

Solutions for Chapter 15.3: INFERENCES ABOUT MEASURES OF CENTRAL TENDENCY

Solutions for Chapter 15.3
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##### ISBN: 9780321757272

Chapter 15.3: INFERENCES ABOUT MEASURES OF CENTRAL TENDENCY includes 23 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Statistics: Informed Decisions Using Data was written by and is associated to the ISBN: 9780321757272. This textbook survival guide was created for the textbook: Statistics: Informed Decisions Using Data , edition: 4. Since 23 problems in chapter 15.3: INFERENCES ABOUT MEASURES OF CENTRAL TENDENCY have been answered, more than 142304 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Assignable cause

The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

• Block

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

• Categorical data

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

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal 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.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Correction factor

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• Covariance matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• 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.

• 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

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Discrete distribution

A probability distribution for a discrete random variable

• Empirical model

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Exponential random variable

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

• 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.

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