One Population
Hypothesis
Testing- Normally
Distributed or
Large n
Population Mean μ
(are the population
means comparable?)
Population Proportion
π
(The chance an
outcome will be
selected)
σ known
σ unknown
Is the population
normally distributed?
Is the population
normally distributed?
Yes
No
No
Is nπ ≥ 5
and n (1-π) ≥ 5
Yes
No
Yes
Convert to
Underlying
Binomial
Distribution
Is n≥30
Yes
Is n≥30
No
Use z test
p-π0
z=
σp
Yes
z-test, with test statistic
Use t test
Use distribution
free test
μ0 is from H0
sxbar= s/√n
df=n-1
Remember degrees of freedom
is for non-normal distributions,
and compensates for the lack of
normality. See pg. 318 for
assumptions
Hypothesis Testing
1. Formulate the null and alternative hypothesis.
2. Select (or find the given) significance level.
3. Select the test statistic and calculate its value
4. Identify the critical value for the test statistic
and state the decision rule
5. Compare the calculated and critical value
6. State the implications.
Confidence Interval
Hypothesis Testing for Two Sample Means
Remember that these are for independent samples.
Hypotheis
Test
μ1-u2
Are the population
standard
deviations equal?
No
For any
sample size
Yes
Compute the pooled
estimate of the common
variance
Only if
n1 and n2
both ≥ 30
Perform t-test for
A z-test approximation can be
unequal variances
performed where
(
)-(μ1-u2)
(
)-(μ1-u2)
with s21 and s22 as estimates
of σ21 = σ22
u1-u2 from H0
and perform the pooled
variances t-test
(
)-(μ1-u2)
Test assumes samples
are from normal
populations with equal
standard deviations.
Section 11.4
See Note 3
u1-u2 from H0
See Note 11.3
And note 2
u1-u2 from H0
See section 11.2
Chi Squared Decision Tree
11.7 summary here!
Test Decision Tree
One
Mean
To compare
one mean to
an expected
value
Two
Independent
Means
To compare
two means to
see if they are
meeting a
similar
standard
Procedure
1. Create H0
a. (e.g. m=m0)
2. Calculate di for each
data point
3. Rank according to |
di|
4. Sort ranks according
to data being R+/R5. Sum R+
6. Compare test statistic
for H0 to critical
value
One
a. W (table
Sample
should be
provided
OR
b. Z-test
Wilcoxon signed
rank
approximatio
test, one nsample
See pg. 510
One
Proportion
Goodness
of
Fit
ANOVA
To compare
the observed
chance of
something
happening to
the expected
chance
ofhappening
To determine if two
samples are drawn
from the same
population or the
two samples are
distributed
similarly
To compare
the means of
more than
two samples
Two
Dependent
Means
Non Parametric
Methods
Regression
To compare
the means of
two related
samples like
before/after
For data that
does not fit
the
assumptions
of normality
and sample
size (n), here
rank is
substituted
for actual data
values.
To attempt to
see if data
points follow
a trend and
how much of
the data that
trend can
explain
Procedure
1. Create H0 (eg
Procedure
md=0 , where md
1. Create H0
Non Paramteric= the population
(m1=m2)
Methods median of di= xi2. Designate the
yi)
smaller of the
two samples as
2. Calculate xi-yi
Two
sample 1
3. Rank |di| and
Samples
3.
Rank the pooled
categorize as R+
data
or RSamples are … 4. Sum the ranks
4. Sum R+
from sample 1
5. Compare to W
to get ΣR1=W
table or use Z5. Compare
to
Wilcoxon signed rank
Wilcoxon
rank sum
test
critical
value
test, paired
samples
test
Dependent
Independent
approximation