AP STATISTICS
LESSON 10 – 2
DAY 2
MORE DETAIL: STATING HYPOTHESES
ESSENTIAL QUESTION:
How are hypotheses created and
what procedures are different in
one-sided and two sided tests?
Objectives:
• To create hypotheses for significance
tests.
• To do the calculations involved with onesided and two-sided significance tests.
More Detail: Stating
Hypotheses
• The first step in a test of significance is to
state a claim that we will try to find
evidence against. This claim is our null
hypotheses.
• The alternative hypotheses, Ha is the claim
about the population that we are truing to
find evidence for.
Null Hypotheses Ho
• The statement being tested in a test of
significance is called the null hypotheses.
• The test of significance is designed to
asses the strength of the evidence against
the null hypotheses. Usually the null
hypotheses is a statement of “no effect” or
“ no difference.”
One-sided and Two Sided
Hypotheses
Ho : μ = 0
H a: μ > 0
This alternative hypotheses is one-sided.
Ho: μ = 0
H a: μ ≠ 0
The direction is not specified so it is a two
sided hypotheses.
Example 10.10
Page 565
Studying Job Satisfaction
Does the job satisfaction of assembly workers differ
when their work is machine-paced rather than selfpaced?
One study chose 28 subjects at random from a group of
women who worked at assembling electronic devices.
Half of the subjects were assigned at random to each of
two groups.
Both groups did similar assembly work, but one work
setup allowed workers to pace themselves and the other
featured an assembly line that at a fixed time intervals so
that the workers were paced by machine.
One-sided vs. Two-sided
• Always state Ho and Ha in terms of population
parameters.
• It is not always easy to decide whether Ha should
be one-sided or two sided. In the case of
Example 10.10 all that is stated is that there is a
difference.
• If you do not have a specific direction firmly in
mind in advance, use a two-sided alternative.
More detail: P-values and
Statistical Significance
• A test of significance assess the evidence
against the null hypotheses by giving a
probability, the P-value.
• If the sample statistic falls far from the
value of the population parameter
suggested by the null hypotheses in the
direction specified by the alternative
hypotheses, it is good evidence against Ho
in favor of Ha.
P-value
The probability, computed assuming that
Ho is true, that the observed outcome
would take a value as extreme or more
extreme than that actually observed is
called the P-value of the test.
The smaller the P-value is, the stronger is
the evidence against Ho provided by the
data.
Final step in Assessing
Significance Tests
We can compare the P-value with a fixed value that we
regard as decisive.
This amounts to announcing in advance how much
evidence against Ho we will insist on.
The decisive value of P is called the significance level.
We write it as α, the Greek letter alpha.
If we choose α = .05, we are requiring that the data give
evidence against Ho so strong that it would happen no
more than 5% of the time.
If α = .01, we are insisting on stronger evidence against
Ho that we insist on evidence so strong it only happens
1% of the time.
Statistical significance
• If the P-value is a small or smaller than alpha, we say that
the data are statistically significant at level α.
• “Significant” in the statistical sense does not mean
“important.”
It means simply “not likely to happen just by chance.” The
significance level α makes “not likely” more exact.
• Significance level 0.01 is often expressed by the
statement”
“The results were significant (P < 0.01)”