Hypothesis Testing
with z Tests
Chapter 7
The z Table
> Benefits of standardization: allowing fair
comparisons
> z table: provides percentage of scores
between the mean and a given z score
Raw Scores, z Scores, and
Percentages
> Step 1: Convert raw score to z score
> Step 2: Look up area in Table
• The table presents area between the Mean
and z and beyond the mean and z.
From Percentages to z Scores
> Step 1: Use the z table in reverse,
taking a percentage and converting it
into a z score.
> Step 2: Convert the z score to a raw
score using the formula.
Sketching the Normal Curve
> The benefits of sketching the normal
curve:
• Stays clear in memory; minimizes errors
• Practical reference
• Condenses the information
The Standardized z Distribution
Calculating the Percentile for a
Positive z Score
Calculating the Percentage Above
a Positive z Score
Calculating the Percentage at
Least as Extreme as Our z
Score
Calculating the Percentile for a
Negative z Score
Calculating the Percentage
Above a Negative z Score
Calculating the Percentage at
Least as Extreme as Our z Score
Calculating a Score from a
Percentile
Check Your Learning
> If the population mean is 10 and the
standard deviation is 2:
• What is the percentile rank of a sample
mean of 6? of 11?
• What percentage of the samples would
score higher than a score of 6? of 11?
The Assumptions and the Steps of
Hypothesis Testing
> Requirements to conduct analyses
• Assumption: characteristic about a
population that we are sampling necessary
for accurate inferences
Parametric v. Nonparametric
Tests
> Parametric tests: inferential statistical test
based on assumptions about a population
> Nonparametric tests: inferential statistical
test not based on assumptions about the
population
An Example of the z Test
> The z test
• When we know the population mean and
the standard deviation
> The z test
• The six steps of hypothesis testing
> H0, H1
> One-tailed vs. two-tailed tests
Determining Critical Values for a z
Distribution – One tailed or twotailed test for significance?
Making a Decision
Check Your Learning
> IQ scores are designed to have a mean
of 100 and a standard deviation of 15.
• Assume the class mean is 114.
• Go through the six steps of hypothesis
testing.
“Dirty” Data
> “Dirty” Data: Missing data, misleading data, and
outliers
> Misleading data: The
famous butterfly ballot
used in Florida during
the 2000 presidential
election showed the
of the arrangement of
items on a page.
Cleaning “Dirty” Data
> Judgment calls need to be made.
> The best solution is to report everything
so that other researchers can assess
the trade-offs.
> The best way to address the problem of
dirty data is replication.