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Chapter 13

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Chapter 13

Sampling: Final and Initial Sample-Size Determination

Figure 13.1 Relationship of Sample Size Determination to the Previous Chapters and the Marketing Research Process

Relationship to

Previous Chapters

Relationship to Marketing

Research Process

Focus of This

Chapter

- Research Design Components (Chapter 3)
- Sampling Design Process (Chapter 12)

- Statistical Approach to Determining Sample Size
- Adjusting the Statistically Determined Sample Size

Problem Definition

Approach to Problem

Research Design

Field Work

Data Preparation

and Analysis

Report Preparation

and Presentation

Figure 13.2 Final and Initial Sample Size Determination: An Overview

Opening Vignette

Definitions and Symbols

Table 13.1

The Sampling Distribution

Figs 13a.1-13a.3

Appendix 13a

Statistical Approach to Determining Sample Size

What Would You Do?

Be a DM! Be an MR! Experiential Learning

Fig 13.3

Confidence Interval Approach

Table 13.2

Fig 13.4

Proportions

Means

Adjusting the Statistically Determined Sample Size

Application to Contemporary Issues (Fig 13.5)

International

Technology

Ethics

- Parameter: A parameter is a summary description of a fixed characteristic or measure of the target population.A parameter denotes the true value which would be obtained if a census rather than a sample was undertaken.
- Statistic: A statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter.
- Random sampling error: The error when the sample selected is an imperfect representation of the population of interest.

- Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter.
- Confidence interval: The confidence interval is the range into which the true population parameter will fall, assuming a given level of confidence.
- Confidence level: The confidence level is the probability that a confidence interval will include the population parameter.

Table 13.1

Symbols for Population and Sample Variables

Confidence Interval

Approach

Means

Proportions

Figure 13.3 The Confidence Interval Approach and Determining Sample Size

The confidence interval is given by

We can now set a 95% confidence interval around the sample mean of $182.

The 95% confidence interval is given by

+ 1.96

= 182.00 + 1.96(3.18) = 182.00 + 6.23

Thus the 95% confidence interval ranges from $175.77 to $188.23.

0.475

0.475

_

_

_

XL

X

XU

Figure 13.4 95% Confidence Interval

Table 13.2

Sample Size Determination for Means and Proportions

Table 13.2 (Cont.)

Sample Size Determination for Means and Proportions

A sample size of 400 is enough to represent China’s more than 1.3 billion people or the more than 300 million American people.

The sample size is independent of the population size for large populations.

Incidence rate refers to the rate of occurrence or the percentage of persons eligible to participate in the study.

In general, if there are c qualifying factors with an incidence of Q1, Q2, Q3, ...QC, each expressed as a proportion,

Incidence rate= Q1 x Q2 x Q3....x QC

Initial sample size= Final sample size

Incidence rate x Completion rate

Figure 13A.1Finding Probabilities Corresponding to Known Values

Area is 0.3413

Area between µ and µ + 1

s

= 0.3413

s

= 0.4772

Area between µ and µ + 2

s

= 0.4986

Area between µ and µ + 3

X Scale

Figure 13A.2Finding Values Corresponding to Known Probabilities

Area is 0.500

Area is 0.450

Area is 0.050

X Scale

X

50

Z Scale

Z = -1.645

0

Figure 13A.3Finding Values Corresponding to Known Probabilities: Confidence Interval

Area is 0.475

Area is 0.475

Area is 0.025

Area is 0.025

X Scale

X

50

Z Scale

Z = 1.96

Z = -1.96

0