Sampling Distribution and Estimation

______: A subset of population used to investigate the unknown probability distribution.

Sample

_____ error is the inevitable result of basing an inference on a random sample rather than on the entire population.

Sampling

____: Probability distribution of a statistic.

Sampling Distribution

_____: A property of a sample from the population.

Statistic

_____ sampling differs from SRS in that each element has an equal chance of being selected but each sample does not have an equal chance of being selected.

Systematic

Elements are selected from the population at a uniform interval that is measured in time, order, or space.

Systematic Sampling

Nonsampling _____ is quite different and can occur for a variety of reasons

error

the specific values of this variable (estimator) is an ____

estimate.

An _____ is a sample statistic, a random variable, used to estimate a population parameter

estimator

It is ____ that an estimator 'truly estimate' the population parameter it is supposed to estimate

important

An _____ estimate describes a range of values within which a population parameter is likely to lie. [Will be discussed later]

interval

An ______ estimate describes a range of values within which a population parameter is likely to lie.

interval

The means of all possible samples of a fixed size n from some population will form a distribution that we call the sampling distribution of the ____

mean.

•When the population is normally distributed, the sampling distribution of the mean is also _____

normal

A ____ estimate is a single number derived from sample data that is used to estimate the value of an unknown population parameter.

point

•Expected value of the sample mean is the _____ mean, µ

population

•A _____ plan states: -its objectives -target population -population frame (the list from which the sample is selected) -operational procedures for collecting data -statistical tools for data analysis

sampling

A ______ random sample of size n is one where each possible sample of size n has the same chance of being chosen.

simple

The standard deviation of the distribution of a sample statistic is known as the _____ error of the statistic.

standard

Often population parameter σ is unknown. Therefore, we compute ______ using s∕√n

standard error

•Standard deviation of the sample mean, called the ____ of the mean, is σ∕√n

standard error

In a ______ sample the population is divided into relatively homogeneous groups (non-overlapping groups) or strata, e.g. geographical areas, age-groups, genders. A sample is taken from each stratum, and when this sample is a simple random sample it is referred to as stratified random sampling.

stratified

ØLike normal distribution, t-distribution is _____

symmetrical.

ØWhen: 1.Sample size, n < 30 2.Population standard deviation (σ) is unknown

t-Distribution

______ is flatter than normal distribution, and there is a different t-distribution for every possible sample size.

t-distribution

ØWe use ______ with the assumption that the population is normal or approximately normal.

t-distribution

If the expected value of an estimator equals the population parameter it is intended to estimate, the estimate is said to be _____

unbiased

When: 1.Sample size, n > 30 (can be n<30) 2.Population standard deviation (σ) is known

z-distribution

_____ sampling - samples are selected based on the ease with which the data can be collected

§Convenience

_____ sampling - expert judgment is used to select the sample

§Judgment

_____ error—occurs when the responses to the questions do not reflect what the investigator had in mind (e.g., when questions are poorly worded).

•Measurement

_____ responses—are particularly a problem when there are sensitive questions in a questionnaire.

•Nontruthful

____ is the foundation of statistical analysis.

•Sampling

______ - a description of the approach that is used to obtain samples from a population prior to any data collection activity.

•Sampling plan

____ response bias—occurs when the subset of people who respond to a survey differs in some important respect from all potential respondents.

•Voluntary

The ____ states that: When an infinite number of random samples are drawn from a population with mean µ and standard deviation σ, the sampling distribution of the mean is approximately normal, and the approximation improves as the sample size increases (n ≥ 30).

Central Limit Theorem

_____ involves assessing the value of an unknown population parameter - mean, proportion, or variance - using sample data.

Estimation

______: A list of all members, called sampling units, in the population.

Frame

C.I. for a Mean (σ ______) - Steps Step 1: Determine the right Probability Distribution for the Sampling Distribution. Step 2: State the Desired Level of Confidence (C.L.) Step 3: Calculate the C.I. and Confidence Limits i.Calculate the standard error of mean (σ_x ̅ ): 〖σ_x ̅ =σ〗∕√n ii.Identify the Critical Value of z_(α∕2) [What is α?] iii.Calculate the C.I. and Confidence Limits: C.I. 〖=x ̅±z_(α∕2) (σ〗_x ̅ ) ● Step 4: Draw a Conclusion About the C.I.

Known

______: A property of a population or a probability distribution.

Parameter

_____: The set of all members (from a particular probability distribution) about which a study intends to make inferences.

Population

_________ Methods §Simple random sampling §Systematic (periodic) sampling §Stratified sampling §Cluster sampling

Probabilistic

C.I. for a _____ ØOften, we are interested in the proportion of observations in a sample that has a certain characteristics. Examples - ØCategorical variables - gender (M or F), education (high school, college, post-graduate), and so on. ØCorrectly complete Medicare forms. ØA customer's account is at least two months overdue. ØAn unbiased estimator of population proportion (π) is the statistic, sample proportion, p ̂=x⁄n , where x is the number in the sample having the desired characteristics.

Proportion

______: One in which the members of the sample are chosen at random from the population. Each member has an equal likelihood of selection.

Random Sample

C.I. for a Mean (σ ______) - Steps Step 1: Determine the Right Probability Distribution for the Sampling Distribution. Step 2: State the Desired Level of Confidence (C.L.) Step 3: Calculate the C.I. and Confidence Limits i.Calculate the standard error of mean (s_x ̅ ): 〖s_x ̅ =s〗∕√n ● ii.Compute df and Identify the Critical Value of t_(α∕〖2,n-1〗) i.Calculate the C.I. and Confidence Limits: C.I. 〖=x ̅±t_(α∕〖2,n-1〗) (s〗_x ̅ ) ● Step 4: Draw a Conclusion About the C.I.

Unknown

In general the size of the sample in each stratum is taken in proportion to the size of the stratum. This is called proportional ______

allocation.

•Nonresponse _____ —occurs when a portion of the sample fails to respond to the survey.

bias

In _____ sampling, the population is separated into clusters, such as cities or city blocks, and then a simple random sample of the clusters is selected.

cluster

The ______ (C.I) is a range or interval of values that has a stated probability of containing unknown population parameter.

confidence interval

The probability that we associate with an interval estimate is called the ______ (C.L.). This probability indicates how confident we are that the interval estimate will include the population parameter.

confidence interval

______can be defined as the number of values we can choose freely i.e. (n-1), where n is the sample size

degrees of freedom

ØAn additional parameter distinguishes different t-distributions, ____ (df).

degrees of freedom