- 4.11.1E: Bottles filled by a certain machine are supposed to contain 12 oz o...
- 4.11.2E: A 500-page book contains 250 sheets of paper. The thickness of the ...
- 4.11.3E: ?A commuter encounters four traffic lights each day on her way to w...
- 4.11.4E: Among all the income-tax forms filed in a certain year, the mean ta...
- 4.11.5E: Bags checked for a certain airline flight have a mean weight of 15 ...
- 4.11.6E: The amount of warpage in a type of wafer used in the manufacture of...
- 4.11.7E: The time spent by a customer at a checkout counter has mean 4 minut...
- 4.11.8E: Drums labeled 30 L are filled with a solution from a large vat. The...
- 4.11.9E: The temperature of a solution will be estimated by taking n indepen...
- 4.11.10E: Among the adults in a large city, 30% have a college degree. A simp...
- 4.11.11E: In a process that manufactures bearings, 90% of the bearings meet a...
- 4.11.12E: A machine produces 1000 steel O-rings per day. Each ring has probab...
- 4.11.13E: Radioactive mass A emits particles at a mean rate of 20 per minute,...
- 4.11.14E: The concentration of particles in a suspension is 30 per ml.a. What...
- 4.11.15E: The concentration of particles in a suspension is 50 per mL. A 5 mL...
- 4.11.16E: ?A battery manufacturer claims that the lifetime of a certain type ...
- 4.11.17E: A new process has been designed to make ceramic tiles. The goal is ...
- 4.11.18E: The manufacture of a certain part requires two different machine op...
- 4.11.19E: Seventy percent of rivets from vendor A meet a certain strength spe...
- 4.11.20E: ?Radiocarbon dating: Carbon- 14 is a radioactive isotope of carbon ...
Solutions for Chapter 4.11: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
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
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
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.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
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.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
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 .
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
Another name for factors that are arranged in a factorial experiment.
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Error of estimation
The difference between an estimated value and the true value.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
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.