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

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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

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:

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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