In this chapter, students will be able to: Learn the financial and statistical issues in the determination of sample size, discover the methods for determining sample size, gain an appreciation of a normal distribution, understand population, sample, and sampling distribution, distinguish between point and interval estimates, recognize problems involving sampling means and proportions.
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1 To learn the financial and statistical issues in
the determination of sample size
2 lo discover the methods for determining
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Determining Sample Size The financial and statistical
sample size
Financial, Statistical, and Managerial Issues
As a general rule:
The larger the sample, the smaller the sampling error
Larger samples cost more; however the sampling error
decreases at a rate equal to the square root of the
relative increase in sample size
Before trying to determine the size of the sample, the confidence intervals need to be decided
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Methods for Determining The financial and statistical
Sample Size issues in the determination of
constraints force the researcher to explore and consider the value of information in relation to its cost
Rules of Thumb
- Desired sampling error - Similar Studies
- Past experience - A gut feeling
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Methods for Determining To discover the methods for
| Sample Size | determining sample size
Number of Subgroups To Be Analyzed
The sample should contain at least 100 respondents in each major subgroup
Traditional Statistical Methods
¢ An estimate of the population standard deviation
¢ The acceptable level of sampling error
¢ The desired level of confidence that the sample will fall within a certain range of the true population values
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The Normal Distribution T O gain an appreciation of a
| | normal distribution
General Properties for the Normal Distribution
Crucial to Classical Statistical Inference
Reasons For Its Importance
¢ Many variables have probability distributions that are close to the normal distribution
¢ Central Limit Theorem—distribution of a large number
of sample means or sample proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn
Trang 81 The normal distribution is bell-shaped and has only one mode
2 Symmetrical about the mean
3 Uniquely defined by its mean and standard deviation
4 The total area is equal to one
5 The area between any two values of a variable equals the
probability of observing a value in that range when randomly selecting an observation from the distribution
6 The area between the mean and a given number of standard deviations from the mean is the same for all normal
distributions
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The Normal Distribution To gain an appreciation of
| | a normal distribution
The Standard Normal Distribution
°ồ The same features as any normal distribution
¢ The mean is equal to zero
¢ The standard deviation is equal to one
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= mean of the variable standard deviation of the variable
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Sampling Distributions To understand population, sample,
| Of The Mean | and sampling distributions
Sampling Distribution of the Sample Mean
A frequency distribution of the means of many sample means from a given population
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Sampling Distributions To understand population, sample,
| Of The Mean | and sampling distributions
lí the samples are sufficiently large and random, the
resulting distribution of sample means will approximate a
normal distribution
The distribution of the means of a large number of random samples taken from virtually any population approaches a normal distribution with a mean equal to anda standard deviation equal to:
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m——— x Learning Objectives
Sampling Distributions To understand population, sample,
| Of The Mean | and sampling distribution
The Standard Error of the Mean
Applies to the standard deviation of a distribution of sample means
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ee ~—s Learning Objectives
Sampling Distribution of To understand population, sample,
| the Mean | and sampling distribution
Making Inferences on the Basis of a Single Sample
A 68 percent probability that any one sample from a
population will produce an estimate of the population mean that is within plus or minus one standard deviation of the
population mean
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Sampling Distributions To distinguish between point and
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Sampling Distribution of To recognize problems involving
| the Proportion | sampling means and proportions
A relative frequency distribution of the sample proportions of
a large number of random samples of a given size drawn
from a particular population
1 Approximates a normal distribution
2 The mean proportion is equal to the population
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Sampling Distribution of To recognize problems involving
| the Proportion | sampling means and proportions
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es = Learning Objectives
Determining Sample Size To recognize problems involving
Problems Involving Means
The formula for calculating the required sample size for problems that involve the estimation of a mean:
= population standard deviation
E = acceptable amount of sampling error
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es = Learning Objectives
Determining Sample Size To recognize problems involving
Problems Involving Proportions
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Determining Sample Size To recognize problems involving
Determining Sample Size for Stratified and Cluster
Sample
¢ Beyond the scope of this text
Determining How Many Sample Units You Need
¢ Don't want to pay for more numbers than needed
¢ Don't want to run out of numbers.
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Determining Sample Size To recognize problems involving
Population Size and Sample Size
Make an adjustment in the sample size if the sample size is more than 5 percent of the size of the total population
Finite Population Correction (FPC)
An adjustment in cases where the sample is expected to be equal to 5 percent or more of the total population (N-n) / (N-1)
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Determining Sample Size To recognize problems involving
Adjusting for a sample that is 5 percent or more of the
population and dropping the independence assumption:
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es = Learning Objectives
Determining Sample Size To recognize problems involving
Heducing the required sample size using the Finite
Population Correction
nN N+n -1
where:
n' = revised sample size
n = original sample size
N = population size
Trang 24| SUMMARY |
¢ Determining Sample Size for Probability Samples
¢ Methods for Determining Sample Size
* The Normal Distribution
¢ Population, Sample, and Sampling Distributions
¢ Sampling Distribution of the Mean
¢ Sampling Distribution of the Proportion
¢ Sample Size Determination
¢ Statistical Power
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Copyright © 2004 John Wiley & Sons, Inc.