- Chapter 1: The Role of Statistics and the Data Analysis Process
- Chapter 10: Hypothesis Testing Using a Single Sample
- Chapter 11: Comparing Two Populations or Treatments
- Chapter 12: The Analysis of Categorical Data and Goodness-of-Fit Tests
- Chapter 13: Simple Linear Regression and Correlation: Inferential Methods
- Chapter 14: Multiple Regression Analysis
- Chapter 15: Analysis of Variance
- Chapter 2: Collecting Data Sensibly
- Chapter 3: Graphical Methods for Describing Data
- Chapter 4: Numerical Methods for Describing Data
- Chapter 5: Summarizing Bivariate Data
- Chapter 6: Probability
- Chapter 7: Random Variables and Probability Distributions
- Chapter 8: Sampling Variability and Sampling Distributions
- Chapter 9: Estimation Using a Single Sample
Introduction to Statistics and Data Analysis (with CengageNOW Printed Access Card) (Available Titles CengageNOW) 3rd Edition - Solutions by Chapter
Full solutions for Introduction to Statistics and Data Analysis (with CengageNOW Printed Access Card) (Available Titles CengageNOW) | 3rd Edition
Introduction to Statistics and Data Analysis (with CengageNOW Printed Access Card) (Available Titles CengageNOW) | 3rd Edition - Solutions by ChapterGet Full Solutions
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.
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
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.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
A distribution with two modes
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Another term for the conidence coeficient.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
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.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Another name for a cumulative distribution function.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
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.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.