- 6.15.1: Refer to Exercise 6 in Section 5.10. Let represent the population m...
- 6.15.2: Refer to Exercise 6 in Section 5.10. Let represent the population m...
- 6.15.3: In the lettuce yield example presented on page 499, would it be a g...
- 6.15.4: It is suspected that using premium gasoline rather than regular wil...
- 6.15.5: For the lettuce yield data (page 499), it is thought that the yield...
- 6.15.6: Refer to Exercise 4. Perform a randomization test to determine whet...
- 6.15.7: A certain wastewater treatment method is supposed to neutralize the...
- 6.15.8: This exercise requires ideas from Section 2.6. In a two-sample expe...
- 6.15.9: This exercise continues Exercise 9 in the Supplementary Exercises f...
- 6.15.10: A population geneticist is studying the genes found at two differen...
- 6.15.11: Hypothesis Testing
Solutions for Chapter 6.15: Using Simulation to Perform Hypothesis Tests
Full solutions for Statistics for Engineers and Scientists | 4th 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
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
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
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
The joint probability distribution of two random variables.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A probability distribution for a continuous random variable.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
Formulas used to determine the number of elements in sample spaces and events.
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 .
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
A matrix that provides the tests that are to be conducted in an experiment.
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
The variance of an error term or component in a model.
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.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r