Solutions for Chapter 4.2: Elementary Statistics 12th Edition

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

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

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

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

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

A continuous random variable with range of a inite interval and a constant probability density function.

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Another name for a probability density function

Another name for a cumulative distribution function.

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.

The variance of an error term or component in a model.

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

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

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

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.

A signal from a control chart when no assignable causes are present

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.

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