- 9.4.1E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.2E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.3E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.4E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.5E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.6E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.7E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.8E: (In some of the exercises that follow, we must make assumptions, su...
- 9.4.9E: (In some of the exercises that follow, we must make assumptions, su...
- 188.8.131.52-1: For the data given in Example 9.4-1, test the hypothesis HA: 1 = 2 ...
- 184.108.40.206-2: With a = 3 and b = 4, find , i, and j if ij, i = 1, 2, 3 and j = 1,...
- 220.127.116.11-3: We wish to compare compressive strengths of concrete corresponding ...
- 18.104.22.168-4: Show that the cross-product terms formed from (Xi X), (Xj X), and (...
- 22.214.171.124-5: A psychology student was interested in testing how food consumption...
- 126.96.36.199-6: With a = 3 and b = 4, find , i, j, and ij if ij, i = 1, 2, 3 and j ...
- 188.8.131.52-7: In order to test whether four brands of gasoline give equal perform...
- 184.108.40.206-8: There is another way of looking at Exercise 9.3-6, namely, as a two...
- 220.127.116.11-9: Ledolter and Hogg (see References) report that volunteers who had a...
Solutions for Chapter 9.4: More Tests
Full solutions for Probability and Statistical Inference | 9th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
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
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
The variance of the conditional probability distribution of a random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
A probability distribution for a continuous random variable.
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 .
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Discrete random variable
A random variable with a inite (or countably ininite) range.
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).
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The variance of an error term or component in a model.
Estimate (or point estimate)
The numerical value of a point estimator.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
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
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications