- 4.1.1E: What is a probability experiment?
- 4.1.2E: Define sample space.
- 4.1.3E: What is the difference between an outcome and an event?
- 4.1.4E: What are equally likely events?
- 4.1.5E: What is the range of the values of the probability of an event?
- 4.1.6E: When an event is certain to occur, what is its probability?
- 4.1.7E: If an event cannot happen, what value is assigned to its probability?
- 4.1.8E: What is the sum of the probabilities of all the outcomes in a sampl...
- 4.1.9E: If the probability that it will rain tomorrow is 0.20, what is the ...
- 4.1.10E: A probability experiment is conducted. Which of these cannot be con...
- 4.1.19E: Shopping Mall Promotion A shopping mall has set up a promotion as f...
- 4.1.20E: Selecting a State Choose one of the 50 states at random.a. What is ...
- 4.1.21E: Human Blood Types Human blood is grouped into four types. The perce...
- 4.1.23E: Prime Numbers A prime number is a number that is evenly divisible o...
- 4.1.24E: Rural Speed Limits Rural speed limits for all 50 states are indicat...
- 4.1.25E: Gender of Children A couple has three children. Find each probabili...
- 4.1.27E: Craps Game In a game of craps, a player loses on the roll if a 2, 3...
- 4.1.28E: Computers in Elementary Schools Elementary and secondary schools we...
- 4.1.29E: College Debt The following information shows the amount of debt stu...
- 4.1.34E: Federal Government Revenue The source of federal government revenue...
- 4.1.35E: Selecting a Bill A box contains a $1 bill, a $5 bill, a $10 bill, a...
- 4.1.36E: Tossing Coins Draw a tree diagram and determine the sample space fo...
- 4.1.37E: Selecting Numbered Balls Four balls numbered 1 through 4 are placed...
- 4.1.38E: Family Dinner Combinations A family special at a neighborhood resta...
- 4.1.39E: Required First-Year College Courses First-year students at a partic...
- 4.1.40E: Tossing a Coin and Rolling a Die A coin is tossed; if it falls head...
- 4.1.41EC: Distribution of CEO Ages The distribution of ages of CEOs is as fol...
- 4.1.42EC: Tossing a Coin A person flipped a coin 100 times and obtained 73 he...
- 4.1.43EC: Medical Treatment A medical doctor stated that with a certain treat...
- 4.1.44EC: Wheel Spinner The wheel spinner shown here is spun twice. Find the ...
- 4.1.45EC: Tossing Coins Toss three coins 128 times and record the number of h...
- 4.1.46EC: Tossing Coins Toss two coins 100 times and record the number of hea...
- 4.1.47EC: Odds Odds are used in gambling games to make them fair. For example...
Solutions for Chapter 4.1: Elementary Statistics: A Step By Step Approach 9th Edition
Full solutions for Elementary Statistics: A Step By Step Approach | 9th Edition
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).
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
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
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
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
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
Bivariate normal distribution
The joint distribution of two normal random variables
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random 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
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.
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 dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
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 .
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.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
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 that is used to determine properties of the probability distribution of a random variable. See Moment-generating function