- 5.2.1: In a simple random sample of 70 automobiles registered in a certain...
- 5.2.2: During a recent drought, a water utility in a certain town sampled ...
- 5.2.3: A soft-drink manufacturer purchases aluminum cans from an outside v...
- 5.2.4: The article HIV-positive Smokers Considering Quitting: Differences ...
- 5.2.5: The article The Functional Outcomes of Total Knee Arthroplasty (R. ...
- 5.2.6: Refer to Exercise 1. Find a 95% lower confidence bound for the prop...
- 5.2.7: Refer to Exercise 2. Find a 98% upper confidence bound for the prop...
- 5.2.8: Refer to Exercise 4. Find a 99% lower confidence bound for the prop...
- 5.2.9: A random sample of 400 electronic components manufactured by a cert...
- 5.2.10: Refer to Exercise 9. A device will be manufactured in which two of ...
- 5.2.11: When the light turns yellow, should you stop or go through it? The ...
- 5.2.12: In a random sample of 150 customers of a high-speed internet provid...
- 5.2.13: A sociologist is interested in surveying workers in computer-relate...
- 5.2.14: Stainless steels can be susceptible to stress corrosion cracking un...
- 5.2.15: The article A Music Key Detection Method Based on Pitch Class Distr...
- 5.2.16: A stock market analyst notices that in a certain year, the price of...
Solutions for Chapter 5.2: Confidence Intervals for Proportions
Full solutions for Statistics for Engineers and Scientists | 4th Edition
`-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).
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 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
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 chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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 tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
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 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 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 .
Formulas used to determine the number of elements in sample spaces and events.
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.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Another name for a cumulative distribution function.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Exponential random variable
A series of tests in which changes are made to the system under study