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Chapter 11

MKT 500 Chapter Notes - Chapter 11: Frequency Distribution, Null Hypothesis, Standard Deviation

Department
Marketing
Course Code
MKT 500
Professor
Tina West
Chapter
11

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CHAPTER 11 Population Estimates and Hypothesis Testing
THE CONCEPT OF GENERALIZATION
Sample finding: percentage or average or some other value computed with a sample’s data
o If follows proper sampling procedures and ensures sample is good representation of target population, sample
findings are best estimates of their respective population facts
Population fact: defined as the true value when a census of the population is taken and the value is determined using all
members of the population
Generalization: act of estimating a population fact from a sample finding
o Form of logic in which an inference about an entire group is made based on some evidence about that group
o Generalization can draw conclusions from amount of available evidence
When estimates of population values are made, the sample finding is used as the beginning point, and then a range is
computed in which the population value is estimated, or generalized, to fall
GENERALIZING A SAMPLE’S FINDINGS: ESTIMATING THE POPULATION VALUE
Parameter estimation: estimation of population values
o Population parameters designated by ∏ (percent) or μ (mean or average); sample findings are relegated to p
(percent) or x (average or mean)
HOW TO ESTIMATE A POPULATION PERCENTAGE (CATEGORICAL DATA)
Confidence interval: range (lower and upper boundary) into which the researcher believes the population parameter falls
with an associated degree of confidence (typically 95% or 99%)
o General formula for estimation of population percentage is written in notation form
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P = sample percentage
Q = 100% - p
Z = z value for 95% (±1.96) or 99% (±2.58) level of confidence (alpha equals ether 95% or 99% level of confidence)
Sp = standard error of the percentage
Standard error: measure of the variability in a population based on the variability found in the sample
o Examining formula for standard error of the percentage, size of standard error depends on two factors: (1)
variability, denoted as p times q and sample size, n
o Standard error of percentage is larger with more variability and smaller with larger samples
Sampling distribution: sample percentages for all samples plotted as a frequency distribution
Generalization procedures are direct linkages between probability sample design and data analysis
o When making non-statistical generalization, judgment can be swayed by subjective factors, and may not be
consistent
o In statistical estimates, formulas are objective and perfectly consistent, and based on accepted statistical concepts
HOW TO ESTIMATE A POPULATION AVERAGE (METRIC DATA)
If data metric, population average is an appropriate measure of central tendency:
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P = sample percentage
Q = 100% - p
Z = z value for 95% (±1.96) or 99% (±2.58) level of confidence (alpha equals ether 95% or 99% level of confidence)
Sp = standard error of the percentage
Standard error of average is larger with more variability (standard deviation) and smaller with large samples (n)
TESTING HYPOTHESES ABOUT PERCENTAGES OR AVERAGES
Hypothesis: statement about the population parameter based on prior knowledge, assumptions, or intuition
o Hypothesismost commonly takes the form of an exact specification as to what the population value is
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