- 2.5.19: A set of n 10 measurements consists of thevalues 5, 2, 3, 6, 1, 2, ...
- 2.5.20: Suppose you want to create a mental pictureof the relative frequenc...
- 2.5.21: A distribution of measurements is relativelymound-shaped with mean ...
- 2.5.22: A set of data has a mean of 75 and a standarddeviation of 5. You kn...
- 2.5.23: Driving Emergencies The length of time requiredfor an automobile dr...
- 2.5.24: Packaging Hamburger Meat The datalisted here are the weights (in po...
- 2.5.25: Breathing Rates Is your breathing rate normal?Actually, there is no...
- 2.5.26: Ore Samples A geologist collected 20different ore samples, all the ...
- 2.5.27: Social Security Numbers A group of70 students were asked to record ...
- 2.5.28: Social Security Numbers, continued Referto the data set in Exercise...
- 2.5.29: Survival Times A group of laboratory animalsis infected with a part...
- 2.5.30: Survival Times, continued Refer to Exercise2.29. You can use the Em...
- 2.5.31: Timber Tracts To estimate the amountof lumber in a tract of timber,...
- 2.5.32: Tuna Fish, again Refer to Exercise 2.8 anddata set EX0208. The pric...
- 2.5.33: Old Faithful The data below are 30waiting times between eruptions o...
- 2.5.34: The Presidents Kids The tablebelow shows the names of the 43 presid...
- 2.5.35: Voter Attitudes You are a candidate for yourstate legislature, and ...
- 2.5.36: Aaron Rodgers The number of passescompleted by Aaron Rodgers, quart...
- 2.5.37: Suppose that some measurements occur morethan once and that the dat...
- 2.5.38: International Baccalaureate High schoolstudents in an International...
- 2.5.39: A Skewed Distribution To illustrate the utilityof the Empirical Rul...
Solutions for Chapter 2.5: A Check on the Calculation of s
Full solutions for Introduction to Probability and Statistics 1 | 14th 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).
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
See Arithmetic mean.
Bivariate normal distribution
The joint distribution of two normal random variables
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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 method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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.
Another name for factors that are arranged in a factorial experiment.
Another name for a probability density function
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
The amount of variability exhibited by data
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
Exponential random variable
A series of tests in which changes are made to the system under study
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.
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 that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
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 .