- 9-3.1: What is the purpose of the study?
- 9-3.2: Are the samples independent or dependent?
- 9-3.3: What hypotheses would you use?
- 9-3.4: What is(are) the critical value(s) that you would use?
- 9-3.5: What statistical test would you use?
- 9-3.6: How many degrees of freedom are there?
- 9-3.7: What is your conclusion?
- 9-3.8: Could an independent means test have been used?
- 9-3.9: Do you think this was a good way to answer the original question?
- 9-3.1: Classify each as independent or dependent samples. a. Heights of id...
- 9-3.2: Retention Test Scores A sample of non-English majors at a selected ...
- 9-3.3: Improving Study Habits As an aid for improving students study habit...
- 9-3.4: Obstacle Course Times An obstacle course was set up on a campus, an...
- 9-3.5: Sleep Report Students in a statistics class were asked to report th...
- 9-3.6: PGA Golf Scores At a recent PGA tournament (the Honda Classic at Pa...
- 9-3.7: Reducing Errors in Grammar A composition teacher wishes to see whet...
- 9-3.8: Amounts of Shrimp Caught According to the National Marine Fisheries...
- 9-3.9: Pulse Rates of Identical Twins A researcher wanted to compare the p...
- 9-3.10: Assessed Land Values A reporter hypothesizes that the average asses...
- 9-3.11: Instead of finding the mean of the differences between X1 and X2 by...
Solutions for Chapter 9-3: Testing the Difference Between Two Means, Two Proportions, and Two Variances
Full solutions for Elementary Statistics: A Step by Step Approach | 7th Edition
Solutions for Chapter 9-3: Testing the Difference Between Two Means, Two Proportions, and Two VariancesGet 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.
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
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
The probability of an event given that the random experiment produces an outcome in another event.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The variance of the conditional probability distribution of a random variable.
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 parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
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.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function