- 11-1.1: How does the goodness-of-fit test differ from the chi-square varian...
- 11-1.2: How are the degrees of freedom computed for the goodness-of-fit tes...
- 11-1.3: How are the expected values computed for the goodness-of-fit test?
- 11-1.4: When the expected frequencies are less than 5 for a specific class,...
- 11-1.5: Home-Schooled Student Activities Students who are home-schooled oft...
- 11-1.6: Combatting Midday Drowsiness A researcher wishes to see if the five...
- 11-1.7: Music Sales In a recent year, 77.8% of recorded music sales were fu...
- 11-1.8: On-Time Performance by Airlines According to the Bureau of Transpor...
- 11-1.9: Genetically Modified Food AnABC News poll asked adults whether they...
- 11-1.10: Truck Colors In a recent year, the most popular colors for light tr...
- 11-1.11: Assessment of Mathematics Students As part of the Mathematics Asses...
- 11-1.12: Ages of Head Start Program Students The Head Start Program provides...
- 11-1.13: Payment Preference AUSA TODAY Snapshot states that 53% of adult sho...
- 11-1.14: College Degree Recipients A survey of 800 recent degree recipients ...
- 11-1.15: Internet Users A survey was targeted at determining if educational ...
- 11-1.16: Education Level and Health Insurance A researcher wishes to see if ...
- 11-1.17: Paying for Prescriptions Amedical researcher wishes to determine if...
- 11-1.18: Tossing Coins Three coins are tossed 72 times, and the number of he...
- 11-1.19: State Lottery Numbers Select a three-digit state lottery number ove...
Solutions for Chapter 11-1: Test for Goodness of Fit
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition
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
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.
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.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A probability distribution for a continuous random variable.
See Control chart.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
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.
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.
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).
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.
Estimate (or point estimate)
The numerical value of a point estimator.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
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 .
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 .
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