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# Solutions for Chapter 6.5: Large-Sample Tests for the Difference Between Two Means

## Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331

Solutions for Chapter 6.5: Large-Sample Tests for the Difference Between Two Means

Solutions for Chapter 6.5
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##### ISBN: 9780073401331

Chapter 6.5: Large-Sample Tests for the Difference Between Two Means includes 13 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since 13 problems in chapter 6.5: Large-Sample Tests for the Difference Between Two Means have been answered, more than 289095 students have viewed full step-by-step solutions from this chapter. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

Key Statistics Terms and definitions covered in this textbook
• 2 k factorial experiment.

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

• 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

• Attribute control chart

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

• Average

See Arithmetic mean.

• Bimodal distribution.

A distribution with two modes

• Binomial random variable

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

• Central limit theorem

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

• 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.

• Contingency table.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

• 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.

• 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.

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• 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.

• Error sum of squares

In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.

• 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.

• 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.

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