Section 9.2:
What is a Test of Significance?
The Reasoning Behind Statistical Tests
• Statistical inference uses data from a sample to
draw conclusions about a population.
• Tests ask if sample data gives good evidence
against a claim.
Null Hypothesis Ho
• The claim being tested in a statistical test.
• The test is designed to assess the strength of the
evidence against the null hypothesis.
• Also known as a statement of “no effect” or “no
difference”.
• Will contain a statement of equality (≤, ≥, or =).
Alternative Hypothesis Ha
• The statement we hope or suspect is true
(instead of the null hypothesis).
• It is the complement of the null hypothesis.
• Contains a statement of inequality (<, >, or ≠).
How they write the statements…
• Null and alternative hypotheses are written with
▫ μ (represents the population parameter) and
▫ k (represents the claim value)
▫ Such as Ho: μ ≥ k
Ha : μ < k
How would you write it???
• A radio station publicizes that its proportion of
the local listening audience is greater than 39%.
▫ Ho: μ ≤ 39%
▫ Ha: μ > 39%
▫ Which was the claim?
How would you write it???
• A consumer analyst reports that the mean life of
a certain type of car battery is 74 months.
▫ Ho: μ = 74 months
▫ Ha: μ ≠ 74 months
▫ Which was the claim here?
▫ FYI, the claim will not always be Ha.
Demonstration of Ho with Basketball
• If a basketball coach claims each of his players
can hit 80% of their free throws, this is the null
hypothesis. We will test this.
• What is the alternative hypothesis?
• Demonstration will use activity on
www.whfreeman.com/sta
• After each demonstration, we will also be given
their true free throw percentage (which may or
may not be 80%).
Homework
• Homework will be posted online…worksheet
with 6 questions. This is due on block day.
• Remember, if you weren’t here for the 9.1 quiz,
or if I notified you that you were missing another
exam, these will all be made up on block day this
week before the vacation.
• I will also distribute the extra credit assignment
and/or post it online on block day.