Stats Chapter 7
Finite Populations (pg.303)
are often defined by lists such as: -Organization membership roster -Credit card account numbers -Inventory product numbers
Parameters (pg.303)
A numerical characteristic of a population, such as a population mean M, a population standard deviation o, population proportion p, and so on.
Standard Error (pg.319)
The standard deviation of a point estimator.
Sampling Distribution (pg.316)
A probability distribution consisting of all possible values of a sample statistics. -Knowledge of this sampling distributions and its properties will enable us to make portability statements about how close the sample mean -x is to the population mean M.
Unbiased (pg.317)
A property of a point estimator that is present when the expected value of the point estimator is equal to the population parameter it estimates. -Thus, the equation (7.1-pg.317) shows that -x is an unbiased estimator of the population mean M.
Sample Statistic (pg.311)
A sample characteristic, such as a sample mean (-x), a sample standard deviation (s), a sample proportion (-p), and so on. The value of the sample statistic is used to estimate the value of the corresponding population parameter. *Look @ notebook for sample mean, sample standard deviation, and sample proportion formulas.*
Simple Random Sample (Finite Population) (pg.303)
A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size n has the same probability of being selected.
Central Limit (pg.319)
A theorem that enables one to use the normal probability distribution to approximate the sampling distribution of -x whenever the sample size is larger. -In most applications, the sampling distribution of -x can be approximated by a normal distribution whenever the sample size 30 or more. - In cases where the population is highly skewed or outliers are [resent, samples of size 50 may be needed. - The smiling distribution of -x can be used to provide probability information about how close the sample mean -x is to the population mean M.
Frame (pg.302)
Is a list of the elements that the sample will be selected from.
Random Sample (Infinite Population) (pg.308)
Is a sample selected such that the following conditions are satisfied: (1) Each element selected comes form the same population. (2) Each element is selected independently (is to prevent election bias) -Situations involving sampling from an infinite population are usually associated with a process that operates over time. Ex. Parts being manufactured on a production line, reported experimental trials in a laboratory, transactions occurring at a bank, telephone calls arriving at a technical support center, and customers entering a retail store. -Not possible to obtain a list of all elements in the population. As a result, we cannot construct a frame for the population.
Sample (pg.301)
Is a subset of the population -The reason we select a sample is to collect data to make inferences and answer research questions about a population. -The sample results provide only ESTIMATES of the values of the population characteristics. ~The reason is simply that the sample contains only a portion of the population. -With PROPER SAMPLING METHODS, the same results can provide "good" estimates of the population characteristics.
Population (pg.301)
Is the collection of all elements of interest.
Element (pg.301)
Is the entity on which data are collected. Ex. Table 1.1 (pg.6-7) is an element, with 60 nations, the data set contains 60 elements.
Sampled Population (pg.302)
Is the population from which the sample is drawn.
Point Estimate (pg.311)
The numerical value obtained for -x,s, or -p -The value of a point estimator used in a particular instance as an estimate of a population parameter. *Point Estimation is a form of statistical inference.*
Target Population (pg.312)
The population for which statistical inferences such as point estimates are made, It is important for the target population to correspond as closely as possible to the sampled population. -Is the population we want to make inference about. In summary, whenever a sample is used to make inferences about a population we should make sure that the study is designed so that the smiled population and the target ovulation are in close agreement.
Point Estimator (pg.311)
The sample statistic, such as -x,s, -p, that provides the point estimate the population parameter. Ex. The sample mean -x as the point estimator of the population mean M (pg.311).
Sampling Distribution of -p (p-bar) (pg.327)
The sampling distribution of -p is the probability distribution of all possible values of the sample proportion. -To determine how close the sample proportion -p is to the population p, we need to understand the properties of the sampling distribution of -p: the expected value of p, the standard deviation of -p, and the shape or form of the sampling distribution of -p.
Sampling Distribution of -x (x-bar) (pg.317)
The sampling distribution of -x is the portability distribution of all possible values of the sample mean -x. -The sample mean -x is a random variable ad it's portability distribution is called the sampling distribution of -x. -This section describes the properties of the sampling distribution of -x. Just as with other probability distributions we studied, the sampling distribution of -x has an expected value or mean, a standard deviation, and a characteristic shaper or form. *Look @ notebook for EXPECTED VALUE of -x equation (pg.317)* "the mean of all possible -x values" This result shows that with simple random sampling, the expected value or mean of the sampling distribution of -x is equal to the mean of the population.
Finite Population Correction Factor (pg.318)
The term \|(N-n)/(N-n) that is used in the formulas for o-x and o-p whenever a finite population, rather than an infinite population, is being sampled. The generally accepted rule of thumb is to ignore the finite population correction factor whenever n/N<=.05 A finite population is treated as being infinite if n/N<=.o5 *Look @ notebook and pg. 318 for notation and rule*