- 5.4.46: Youngs modulus is a quantitative measure of stiffness ofan elastic ...
- 5.4.47: Refer to Exercise 46. Suppose the distribution is normal(the cited ...
- 5.4.48: The National Health Statistics Reports dated Oct. 22, 2008,stated t...
- 5.4.49: There are 40 students in an elementary statistics class.On the basi...
- 5.4.50: Let X denote the courtship time for a randomly selectedfemalemale p...
- 5.4.51: The time taken by a randomly selected applicant for amortgage to fi...
- 5.4.52: The lifetime of a certain type of battery is normally distributedwi...
- 5.4.53: Rockwell hardness of pins of a certain type is known tohave a mean ...
- 5.4.54: Suppose the sediment density (g/cm) of a randomlyselected specimen ...
- 5.4.55: The number of parking tickets issued in a certain city onany given ...
- 5.4.56: A binary communication channel transmits a sequenceof bits (0s and ...
- 5.4.57: Suppose the distribution of the time X (in hours) spent bystudents ...
Solutions for Chapter 5.4: The Distribution of the Sample Mean
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
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.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
A probability distribution for a continuous random variable.
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A matrix that provides the tests that are to be conducted in an experiment.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Error of estimation
The difference between an estimated value and the true value.
Exponential random variable
A series of tests in which changes are made to the system under study
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
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 signal from a control chart when no assignable causes are present
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
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 harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .