# Solutions for Chapter 8-1: Hypothesis Testing

## Full solutions for Elementary Statistics: A Step by Step Approach | 7th Edition

ISBN: 9780073534978

Solutions for Chapter 8-1: Hypothesis Testing

Solutions for Chapter 8-1
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##### ISBN: 9780073534978

This textbook survival guide was created for the textbook: Elementary Statistics: A Step by Step Approach, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Since 13 problems in chapter 8-1: Hypothesis Testing have been answered, more than 7591 students have viewed full step-by-step solutions from this chapter. Elementary Statistics: A Step by Step Approach was written by Patricia and is associated to the ISBN: 9780073534978. Chapter 8-1: Hypothesis Testing includes 13 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• a-error (or a-risk)

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• 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.

• Conditional variance.

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

• 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

• Contingency table.

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

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• Contrast

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Defect concentration diagram

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

• Deining relation

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

• 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.

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• Erlang random variable

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

• 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.

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• 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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