- 6.5.1: The article Capillary Leak Syndrome in Children with C4A-Deficiency...
- 6.5.2: The article Some Parameters of the Population Biology of Spotted Fl...
- 6.5.3: The article Measurement of Complex Permittivity of Asphalt Paving M...
- 6.5.4: The article Wired: Energy Drinks, Jock Identity, Masculine Norms, a...
- 6.5.5: In a test to compare the effectiveness of two drugs designed to low...
- 6.5.6: Two machines used to fill soft drink containers are being compared....
- 6.5.7: A statistics instructor who teaches a lecture section of 160 studen...
- 6.5.8: Fifty specimens of a new computer chip were tested for speed in a c...
- 6.5.9: Are low-fat diets or low-carb diets more effective for weight loss?...
- 6.5.10: In a certain supermarket, a sample of 60 customers who used a self-...
- 6.5.11: The National Opinion Research Center polled a sample of 92 people a...
- 6.5.12: The following MINITAB output presents the results of a hypothesis t...
- 6.5.13: The following MINITAB output presents the results of a hypothesis t...
Solutions for Chapter 6.5: Large-Sample Tests for the Difference Between Two Means
Full solutions for Statistics for Engineers and Scientists | 4th Edition
Solutions for Chapter 6.5: Large-Sample Tests for the Difference Between Two MeansGet Full Solutions
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
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
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
See Arithmetic mean.
A distribution with two modes
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
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.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
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.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
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.
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.
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.