- 6.1.1: The accompanying data on flexural strength (MPa) forconcrete beams ...
- 6.1.2: The National Health and Nutrition ExaminationSurvey (NHANES) collec...
- 6.1.3: Consider the following sample of observations on coatingthickness f...
- 6.1.4: The article from which the data in Exercise 1 was extractedalso gav...
- 6.1.5: As an example of a situation in which several differentstatis tics ...
- 6.1.6: Urinary angiotensinogen (AGT) level is one quantitativeindicator of...
- 6.1.7: a. A random sample of 10 houses in a particular area,each of which ...
- 6.1.8: In a random sample of 80 components of a certain type,12 are found ...
- 6.1.9: Each of 150 newly manufactured items is examined andthe number of s...
- 6.1.10: Using a long rod that has length m, you are going to layout a squar...
- 6.1.11: Using a long rod that has length m, you are going to layout a squar...
- 6.1.12: Suppose a certain type of fertilizer has an expected yieldper acre ...
- 6.1.13: Consider a random sample X1, , Xn from the pdff(x; u) 5 .5(1 1 ux)2...
- 6.1.14: A sample of n captured Pandemonium jet fighters resultsin serial nu...
- 6.1.15: Let X1, X2, , Xn represent a random sample from aRayleigh distribut...
- 6.1.16: Suppose the true average growth m of one type of plantduring a 1yea...
- 6.1.17: In Chapter 3, we defined a negative binomial rv as thenumber of fai...
- 6.1.18: Let X1, X2, , Xn be a random sample from a pdf f(x)that is symmetri...
- 6.1.19: An investigator wishes to estimate the proportion of studentsat a c...
Solutions for Chapter 6.1: Some General Concepts of Point Estimation
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
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).
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.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
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
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.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Another name for factors that are arranged in a factorial experiment.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.