- 6-4.1: Explain why a normal distribution can be used as an approximation t...
- 6-4.2: (ans) Use the normal approximation to the binomial to find the prob...
- 6-4.3: Check each binomial distribution to see whether it can be approxima...
- 6-4.4: School Enrollment Of all 3- to 5-year-old children, 56% are enrolle...
- 6-4.5: Youth Smoking Two out of five adult smokers acquired the habit by a...
- 6-4.6: Mail Order Amail order company has an 8% success rate. If it mails ...
- 6-4.7: Voter Preference A political candidate estimates that 30% of the vo...
- 6-4.8: Household Computers According to recent surveys, 60% of households ...
- 6-4.9: Female Americans Who Have Completed 4 Years of College The percenta...
- 6-4.10: Population of College Cities College students often make up a subst...
- 6-4.11: Elementary School Teachers Women comprise 80.3% of all elementary s...
- 6-4.12: Telephone Answering Devices Seventy-eight percent of U.S. homes hav...
- 6-4.13: Parking Lot Construction The mayor of a small town estimates that 3...
- 6-4.14: Residences of U.S. Citizens According to the U.S. Census, 67.5% of ...
- 6-4.15: Recall that for use of a normal distribution as an approximation to...
Solutions for Chapter 6-4: The Normal Approximation to the Binomial Distribution
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th 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).
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
A distribution with two modes
Bivariate normal distribution
The joint distribution of two normal random variables
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
See Control chart.
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 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.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
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.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .