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# Solutions for Chapter 7.4: Estimating a Population Standard Deviation or Variance

## Full solutions for Essentials of Statistics | 5th Edition

ISBN: 9780321924599

Solutions for Chapter 7.4: Estimating a Population Standard Deviation or Variance

Solutions for Chapter 7.4
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##### ISBN: 9780321924599

Chapter 7.4: Estimating a Population Standard Deviation or Variance includes 23 full step-by-step solutions. This textbook survival guide was created for the textbook: Essentials of Statistics, edition: 5. Essentials of Statistics was written by and is associated to the ISBN: 9780321924599. Since 23 problems in chapter 7.4: Estimating a Population Standard Deviation or Variance have been answered, more than 15661 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• All possible (subsets) regressions

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• Asymptotic relative eficiency (ARE)

Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• C chart

An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

• Completely randomized design (or experiment)

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• 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.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Defects-per-unit control chart

See U chart

• Degrees of freedom.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

• Deining relation

A subset of effects in a fractional factorial design that deine the aliases in the design.

• Distribution function

Another name for a cumulative distribution function.

• Eficiency

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• Error of estimation

The difference between an estimated value and the true value.

• Event

A subset of a sample space.

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• Generator

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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