# Solutions for Chapter 6-3: The Central Limit Theorem

## Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition

ISBN: 9780073386102

Solutions for Chapter 6-3: The Central Limit Theorem

Solutions for Chapter 6-3
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##### ISBN: 9780073386102

This textbook survival guide was created for the textbook: Elementary Statistics: A Step by Step Approach 8th ed., edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Elementary Statistics: A Step by Step Approach 8th ed. was written by Patricia and is associated to the ISBN: 9780073386102. Chapter 6-3: The Central Limit Theorem includes 30 full step-by-step solutions. Since 30 problems in chapter 6-3: The Central Limit Theorem have been answered, more than 10408 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

• Attribute control chart

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

• 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.

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• Conditional probability density function

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

• Conditional probability distribution

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

• Conidence interval

If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

• Conidence level

Another term for the conidence coeficient.

• Continuous random variable.

A random variable with an interval (either inite or ininite) of real numbers for its range.

• 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 normal distribution function

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

• 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.

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• 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.

• Deming

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

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• 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.

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

• 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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