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
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To distinguish between point and interval estimates
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Determining Sample Size The financial and statistical
for Probability Samples issues in the determination of
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
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Methods for Determining The financial and statistical Sample Size issues in the determination of sample size Budget Available Sample Size—a project is often determined by the available budget
Alternative Data Collection Approaches—budget constraints force the researcher to explore and consider the value of information in relation to its cost
Rules of Thumb
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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
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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
Trang 8Iil000000000000000000000000000000000000000000J L.carrnnc C2bjcc1:vcs The Normal Distribution To gain an appreciation of | | a normal distribution Important Characteristics of the Normal Distribution
1 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
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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
Trang 10Iil000000000000000000000000000000000000000000J L.carrnnc C2bjcc1:vcs The Normal Distribution To gain an appreciation of | | a normal distribution value of the variable - mean of the variable Z= standard deviation of the variable x - 7 - —— where
X = value of the variable = mean of the variable
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Sampling Distributions To understand population, sample, | Of The Mean | and sampling distributions Population Distribution A frequency distribution of all the elements of a population Sample Distribution A frequency distribution of all the elements of an individual sample
Sampling Distribution of the Sample Mean
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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
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Sampling Distribution of To understand population, sample,
| the Mean | and sampling distribution Basic Concepts 1 A normal distribution 2 Mean equal to the population mean 3 Standard deviation
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
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Sampling Distributions To distinguish between point and
| Of The Mean | interval estimates
Point Estimates
Inferences regarding the sampling error associated with a particular estimate of the population value
Interval Estimate
Inference regarding the likelinood that a population value will fall within a certain range
x= 1 X < <xX+1
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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
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Sampling Distribution of To recognize problems involving
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es = Learning Objectives
Determining Sample Size To recognize problems involving
| | sampling means and proportions
Problems Involving Means
The formula for calculating the required sample size for problems that involve the estimation of a mean: n Z2 2 — _—¬ where: Z = level of confidence expressed in Standard errors
= population standard deviation
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es = Learning Objectives
Determining Sample Size To recognize problems involving
| | sampling means and proportions
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Determining Sample Size To recognize problems involving
| | sampling means and proportions
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
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Determining Sample Size To recognize problems involving
| | sampling means and proportions
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
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Determining Sample Size To recognize problems involving
| | sampling means and proportions
Adjusting for a sample that is 5 percent or more of the population and dropping the independence assumption:
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Determining Sample Size To recognize problems involving
| | sampling means and proportions
Heducing the required sample size using the Finite Population Correction nN N+n -1 where:
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¢ 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
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