- 1.1: Walmart Stores Currently, there are 4227 Walmart stores in the Unit...
- 1.2: Whats Wrong? A survey sponsored by the American Laser Centers inclu...
- 1.3: Whats Wrong? A survey included 4230 responses from Internet users w...
- 1.4: Sampling Seventy-two percent of Americans squeeze their toothpaste ...
- 1.5: Percentagesa. The labels on U-Turn protein energy bars include the ...
- 1.6: Why the Discrepancy? A Gallup poll was taken two years before a pre...
- 1.7: Statistical Significance and Practical Significance The Gengene Res...
- 1.8: Marijuana Survey In a recent Pew poll of 1500 adults, 52% of the re...
- 1.9: Marijuana Survey Identify the type of sampling (random, systematic,...
- 1.10: Marijuana Survey Exercise 8 referred to a Pew poll of 1500 adults, ...
- 1.11: Scientific Notation. In Exercises 912, the given expressions are de...
- 1.12: Scientific Notation. In Exercises 912, the given expressions are de...
Solutions for Chapter 1: Introduction to Statistics
Full solutions for Essentials of Statistics | 5th Edition
`-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-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.
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
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.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal 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
The probability of an event given that the random experiment produces an outcome in another event.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A probability distribution for a continuous random variable.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
See Control chart.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
An expression sometimes used for nonlinear regression models or polynomial regression models.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Exponential random variable
A series of tests in which changes are made to the system under study
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials