- 6.1: A fleet of 100 taxis is divided into two groups of 50 cars each to ...
- 6.2: A group of 15 swimmers is chosen to participate in an experiment to...
- 6.3: A new quality-inspection program is being tested to see if it will ...
- 6.4: A new material is being tested for use in the manufacture of electr...
- 6.5: Suppose you have purchased a filling machine for candy bags that is...
- 6.6: Are answer keys to multiple-choice tests generated randomly, or are...
- 6.7: An automobile manufacturer wishes to compare the lifetimes of two b...
- 6.8: Twenty-one independent measurements were taken of the hardness (on ...
- 6.9: There is concern that increased industrialization may be increasing...
- 6.10: The article Modeling of Urban Area Stop-andGo Traffic Noise (P. Pam...
- 6.11: A machine that grinds valves is set to produce valves whose lengths...
- 6.12: Resistors for use in a certain application are supposed to have a m...
- 6.13: A machine manufactures bolts that are supposed to be 3 inches in le...
- 6.14: Electric motors are assembled on four different production lines. R...
- 6.15: Refer to Exercise 14. The process engineer notices that the sample ...
- 6.16: Consider the following two samples: X : 0 2 3 4 10 20 40 100 1000 Y...
- 6.17: The rank-sum test is sometimes thought of as a test for population ...
- 6.18: A new production process is being contemplated for the manufacture ...
- 6.19: Two different chemical formulations of rocket fuel are considered f...
- 6.20: Suppose the Environmental Protection Agency is in the process of mo...
- 6.21: Two machines are used to package laundry detergent. It is known tha...
- 6.22: The article Valuing Watershed Quality Improvements Using Conjoint A...
- 6.23: Anthropologists can estimate the birthrate of an ancient society by...
- 6.24: Deforestation is a serious problem throughout much of India. The ar...
Solutions for Chapter 6: Hypothesis Testing
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
The probability of an event given that the random experiment produces an outcome in another event.
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 two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
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 .
Formulas used to determine the number of elements in sample spaces and events.
Another name for factors that are arranged in a factorial experiment.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Error sum of squares
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.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
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.
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
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
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.
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .