- 7.5.15: Random samples of size n were selectedfrom populations with the mea...
- 7.5.16: Refer to Exercise 7.15.a. If the sampled populations are normal, wh...
- 7.5.17: A population consists of N 5 numbers:1, 3, 5, 6, and 7. It can be s...
- 7.5.18: Refer to Exercise 7.17.a. Use the data entry method in your calcula...
- 7.5.19: A random sample of n observations is selectedfrom a population with...
- 7.5.20: Refer to Exercise 7.19. Plot the standard error ofthe mean (SE) ver...
- 7.5.21: A random sample of size n 49 is selectedfrom a population with mean...
- 7.5.22: Refer to Exercise 7.21. Find the probability thatthe sample mean is...
- 7.5.23: A random sample of size n 40 is selectedfrom a population with mean...
- 7.5.24: Refer to Exercise 7.23. Find the probability thatthe sample mean is...
- 7.5.25: Suppose a random sample of n 25 observationsis selected from a popu...
- 7.5.26: Faculty Salaries Suppose that college facultywith the rank of profe...
- 7.5.27: Measurement Error When research chemistsperform experiments, they m...
- 7.5.28: Tomatoes Explain why the weight of a packageof one dozen tomatoes s...
- 7.5.29: Bacteria in Water Use the Central LimitTheorem to explain why a Poi...
- 7.5.30: Paper Strength A paper manufacturerrequires a minimum strength of 2...
- 7.5.31: Potassium Levels The normal daily humanpotassium requirement is in ...
- 7.5.32: Deli Sales The total daily sales, x, in the delisection of a local ...
- 7.5.33: Normal Temperatures In Exercise 1.67,Allen Shoemaker derived a dist...
- 7.5.34: Sports and Achilles Tendon Injuries Sportsthat involve a significan...
Solutions for Chapter 7.5: The Sampling Distribution of the Sample Mean
Full solutions for Introduction to Probability and Statistics 1 | 14th Edition
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
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.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The mean of the conditional probability distribution of a random variable.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
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 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 .
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
A matrix that provides the tests that are to be conducted in an experiment.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.