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# Solutions for Chapter 5.4: The Distribution of the Sample Mean

## Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition

ISBN: 9781305251809

Solutions for Chapter 5.4: The Distribution of the Sample Mean

Solutions for Chapter 5.4
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##### ISBN: 9781305251809

Since 12 problems in chapter 5.4: The Distribution of the Sample Mean have been answered, more than 79754 students have viewed full step-by-step solutions from this chapter. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Chapter 5.4: The Distribution of the Sample Mean includes 12 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• Bayes’ estimator

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

• Bayes’ theorem

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

• 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.

• 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.

• Conditional probability density function

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

• Continuous distribution

A probability distribution for a continuous random variable.

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• Deming

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

• Design matrix

A matrix that provides the tests that are to be conducted in an experiment.

• 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.

• Exponential random variable

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

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

• 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.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• 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.

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• 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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