- 7-4.1: What distribution must be used when computing confidence intervals ...
- 7-4.2: What assumption must be made when computing confidence intervals fo...
- 7-4.3: Using Table G, find the values for x2 left and x2 right. a. a _ 0.0...
- 7-4.4: Lifetimes ofWristwatches Find the 90% confidence interval for the v...
- 7-4.5: Carbohydrates in Yogurt The number of carbohydrates (in grams) per ...
- 7-4.6: Carbon Monoxide Deaths A study of generationrelated carbon monoxide...
- 7-4.7: Cost of Knee Replacement Surgery U.S. insurers costs for knee repla...
- 7-4.8: Age of College Students Find the 90% confidence interval for the va...
- 7-4.9: New-Car Lease Fees A new-car dealer is leasing various brand-new mo...
- 7-4.10: Stock Prices Arandom sample of stock prices per share (in dollars) ...
- 7-4.11: Number of Homeless Individuals A researcher wishes to find the conf...
- 7-4.12: Home Ownership Rates The percentage rates of home ownership for 8 r...
- 7-4.13: Calculator Battery Lifetimes A confidence interval for a standard d...
Solutions for Chapter 7-4: Confidence Intervals for Variances and Standard Deviations
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition
Solutions for Chapter 7-4: Confidence Intervals for Variances and Standard DeviationsGet Full Solutions
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
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
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
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
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.
See Arithmetic mean.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
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
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
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A probability distribution for a continuous 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 term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
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
Fraction defective control chart
See P chart
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function