# Sample Mean

**Topics:**Sample size, Normal distribution, Sampling

**Pages:**33 (5279 words)

**Published:**October 27, 2012

7-1

Learning Objectives

In this chapter, you learn:

To distinguish between different sampling methods The concept of the sampling distribution To compute probabilities related to the sample mean and the sample proportion The importance of the Central Limit Theorem

7-2

Why Sample?

DCOVA

Selecting a sample is less time-consuming than selecting every item in the population (census).

An analysis of a sample is less cumbersome and more practical than an analysis of the entire population.

7-3

A Sampling Process Begins With A Sampling Frame DCOVA

The sampling frame is a listing of items that make up the population Frames are data sources such as population lists, directories, or maps Inaccurate or biased results can result if a frame excludes certain portions of the population Using different frames to generate data can lead to dissimilar conclusions 7-4

Types of Samples

Samples

DCOVA

Non-Probability Samples

Probability Samples

Judgment

Convenience

Simple Random

Stratified Cluster

Systematic

7-5

DCOVA

In a nonprobability sample, items included are chosen without regard to their probability of occurrence.

In convenience sampling, items are selected based only on the fact that they are easy, inexpensive, or convenient to sample. In a judgment sample, you get the opinions of preselected experts in the subject matter.

TYPES OF SAMPLES: NONPROBABILITY SAMPLE

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Types of Samples: Probability Sample

DCOVA

In a probability sample, items in the sample are chosen on the basis of known probabilities. Probability Samples

Simple Random

Systematic

Stratified

Cluster

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Probability Sample: Simple Random Sample

DCOVA

Every individual or item from the frame has an equal chance of being selected Selection may be with replacement (selected individual is returned to frame for possible reselection) or without replacement (selected individual isn’t returned to the frame). Samples obtained from table of random numbers or computer random number generators. 7-8

Selecting a Simple Random Sample Using A Random Number Table DCOVA Sampling Frame For Population With 850 Items Item Name Item # Bev R. Ulan X. . . . . Joann P. Paul F. 001 002 . . . . 849 850

Portion Of A Random Number Table

49280 88924 35779 00283 81163 07275 11100 02340 12860 74697 96644 89439 09893 23997 20048 49420 88872 08401

The First 5 Items in a simple random sample

Item # 492 Item # 808 Item # 892 -- does not exist so ignore Item # 435 Item # 779 Item # 002

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Probability Sample: Systematic Sample

Decide on sample size: n

DCOVA

Divide frame of N individuals into groups of k individuals: k=N/n Randomly select one individual from the 1st group Select every kth individual thereafter N = 40 n=4 k = 10

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First Group

Probability Sample: Stratified Sample

to some common characteristic

DCOVA

Divide population into two or more subgroups (called strata) according A simple random sample is selected from each subgroup, with sample sizes proportional to strata sizes Samples from subgroups are combined into one This is a common technique when sampling population of voters, stratifying across racial or socio-economic lines.

Population Divided into 4 strata

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Probability Sample Cluster Sample

DCOVA

Population is divided into several “clusters,” each representative of the population A simple random sample of clusters is selected All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique A common application of cluster sampling involves election exit polls, where certain election districts are selected and sampled.

Population divided into 16 clusters.

Randomly selected clusters for sample

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Probability Sample: Comparing Sampling Methods

DCOVA

Simple random sample and Systematic sample Simple to use May...

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