- 9.5.30: A random sample of n 1000 observationsfrom a binomial population pr...
- 9.5.31: A random sample of n 1400 observationsfrom a binomial population pr...
- 9.5.32: A random sample of 120 observations wasselected from a binomial pop...
- 9.5.33: Childhood Obesity According to a survey inPARADE magazine, almost h...
- 9.5.34: Plant Genetics A peony plant with red petalswas crossed with anothe...
- 9.5.35: Early Detection of Breast Cancer Of thosewomen who are diagnosed to...
- 9.5.36: Sweet Potato Whitefly Suppose that 10% ofthe fields in a given agri...
- 9.5.37: Taste Testing In a head-to-head taste test ofstore-brand foods vers...
- 9.5.38: Taste Testing, continued In Exercise 9.37,we tried to prove that th...
- 9.5.39: A Cure for Insomnia An experimenter hasprepared a drug-dose level t...
- 9.5.40: Landlines Passe? According to a new nationwidesurvey from the Pew R...
- 9.5.41: Mans Best Friend The Humane Societyreports that there are approxima...
Solutions for Chapter 9.5: A Large-Sample Test of Hypothesis for a Binomial Proportion
Full solutions for Introduction to Probability and Statistics 1 | 14th Edition
Solutions for Chapter 9.5: A Large-Sample Test of Hypothesis for a Binomial ProportionGet Full Solutions
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).
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
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.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
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 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.
Coeficient of determination
See R 2 .
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
The probability of an event given that the random experiment produces an outcome in another event.
The variance of the conditional probability distribution of a random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Formulas used to determine the number of elements in sample spaces and events.
Another name for a probability density function
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
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.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.