- 14-1.1: Name the four basic sampling techniques. Random, systematic, strati...
- 14-1.2: Why are samples used in statistics?
- 14-1.3: What is the basic requirement for a sample? A sample must be random...
- 14-1.4: Why should random numbers be used when you are selecting a random s...
- 14-1.5: List three incorrect methods that are often used to obtain a sample.
- 14-1.6: What is the principle behind random numbers? Over the long run each...
- 14-1.7: List the advantages and disadvantages of random sampling.
- 14-1.8: List the advantages and disadvantages of systematic sampling.
- 14-1.9: List the advantages and disadvantages of stratified sampling.
- 14-1.10: List the advantages and disadvantages of cluster sampling.
- 14-1.11: Population andArea of U.S. Cities Using the table of random numbers...
- 14-1.12: Rainfall in U.S. Cities Select a sample of 10 cities by the systema...
- 14-1.13: Wind Speeds Select a cluster sample of 10 cities and calculate the ...
- 14-1.14: Are there any characteristics of these data that might create probl...
- 14-1.15: Which method of sampling might be good for this set of data? Choose...
- 14-1.16: Record High Temperatures Choose a different method to select 10 sta...
- 14-1.17: Electoral Votes Select a systematic sample of 10 states and compute...
- 14-1.18: Electoral Votes Divide the 50 states into five subgroups by geograp...
- 14-1.19: Electoral Votes Select a cluster of 10 states and compute the mean ...
- 14-1.20: Many research studies described in newspapers and magazines do not ...
Solutions for Chapter 14-1: Common Sampling Techniques
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition
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
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
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.
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.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
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.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
The response variable in regression or a designed experiment.
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
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Error of estimation
The difference between an estimated value and the true value.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
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.
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 .
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .