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# Solutions for Chapter Chapter 5.3: Fundamentals of Statistics 4th Edition

## Full solutions for Fundamentals of Statistics | 4th Edition

ISBN: 9780321838704

Solutions for Chapter Chapter 5.3

Solutions for Chapter Chapter 5.3
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##### ISBN: 9780321838704

This expansive textbook survival guide covers the following chapters and their solutions. Chapter Chapter 5.3 includes 33 full step-by-step solutions. Since 33 problems in chapter Chapter 5.3 have been answered, more than 290869 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Fundamentals of Statistics, edition: 4. Fundamentals of Statistics was written by and is associated to the ISBN: 9780321838704.

Key Statistics Terms and definitions covered in this textbook
• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Backward elimination

A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

• Bayes’ theorem

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

• 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.

• Chi-square test

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• Conditional mean

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

• Confounding

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

• Conidence coeficient

The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

• 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.

• Cumulative distribution function

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

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• 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.

• 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.

• Fraction defective

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

• Frequency distribution

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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