- 6.15.4E: It is suspected that using premium gasoline rather than regular wil...
- 6.15.1E: Refer to Exercise 6 in Section 5.9. Let p represent the population ...
- 6.15.2E: Refer to Exercise 6 in Section 5.9. Let ? represent the population ...
- 6.15.3E: In the lettuce yield example presented on page 494, would it be a g...
- 6.15.5E: For the lettuce yield data, (page 494) it is thought that the yield...
- 6.15.6E: Refer to Exercise 6. Perform a randomization test to determine whet...
- 6.15.7E: A certain wastewater treatment method is supposed to neutralize the...
- 6.15.8E: This exercise requires ideas from Section 2.6. In a two- sample exp...
- 6.15.9E: This exercise continues Exercise 9 in the Supplementary Exercises f...
- 6.15.10E: A population geneticist is studying the genes found at two differen...
Solutions for Chapter 6.15: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
See Arithmetic mean.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
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.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A subset of a sample space.
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 model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.