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Inference
about?
Official Summary Sheet ADM 2304 Midterm Exam Winter 2020
One group or
two?
One sample
PROPORTIONS
Two
independent
groups
One sample
MEANS
Two
independent
groups
Matched pairs
DISTRIBUTIONS
(one categorical
variable)
INDEPENDENCE
(two categorical
variables)
Sample size
-
One
sample
Many
independent
groups
One sample
Proportions:
𝑧G,⁄, 𝑝I(1 − 𝑝I)
𝑛=
𝐸,
Means:
𝑧G⁄, 𝜎 ,
𝑛=J
L
𝐸
Procedure
1-Proportion
𝑧-Interval
1-Proportion
𝑧-Test
Model
𝑧
Parameter
𝑝
Estimate
Standard error
𝑝̂
𝑝̂ 𝑞&
$
𝑛
𝑝) 𝑞)
(
𝑛
𝑝̂* 𝑞&* 𝑝̂ , 𝑞&,
$
+
𝑛*
𝑛,
2-Proportion
𝑧-Interval
2-Proportion
𝑧-Test
𝑡-Interval
𝑡-Test
2-Sample 𝑡-Test
2-Sampe 𝑡-Interval
Unpooled Variance
2-Sample 𝑡-Test
2-Sampe 𝑡-Interval
Pooled Variance
Paired 𝑡-Test
Paired 𝑡-Interval
Goodness-of-Fit
Homogeneity
𝜒, Test
Independence
𝜒, Test
𝑧
𝑝* − 𝑝,
𝑝̂* − 𝑝̂,
𝑡
df = 𝑛 − 1
𝜇
𝑥̅
𝑝̅𝑞/ 𝑝̅𝑞/
$ + ,
𝑛* 𝑛,
𝑋* + 𝑋,
𝑝̅ =
𝑛* + 𝑛,
𝑠
√𝑛
𝑠, 𝑠 ,
$*+ ,
𝑛* 𝑛,
𝑡
df from technology
𝑡
df = 𝑛* + 𝑛, − 2
𝑡
df = 𝑛 − 1
𝜒,
df = cells −1
,
𝜒
df = (𝑟 − 1)(𝑐 − 1)
𝜇* − 𝜇,
𝑥̅* − 𝑥̅,
𝜇>
𝑑̅
𝑠, 𝑠 ,
$ ; + ;,
𝑛* 𝑛,
(𝑛
−
1)𝑠*, + (𝑛, − 1)𝑠,,
*
𝑠;, =
𝑛* + 𝑛, − 2
𝑠>
√𝑛
A
(𝑂𝑏𝑠 − 𝐸𝑥𝑝),
𝐸𝑥𝑝
Notes
Inference about?
One group or two?
Assumptions
Conditions that support or override them
Individuals are independent.
1. SRS and 𝑛 < 10% of the population.
One sample
Sample is sufficiently large.
2. Successes and failures each ≥ 10.
Groups are independent.
1. Think about how the data were collected.
PROPORTIONS (𝑧)
Data in each group are
2. Both are SRSs and 𝑛 < 10% of populations.
Two groups
independent.
3. Successes and failures each ≥ 10 for both
3. Both groups are sufficiently large.
groups.
One sample
1. Individuals are independent.
1. SRS and 𝑛 < 10% of the population.
(df = 𝑛 − 1)
2. Population has a Normal model.
2. Histogram is unimodal and symmetric*.
Two independent
1. Groups are independent.
1. Think about the design.
samples
2. Data in each group are
2. Both are SRSs and 𝑛 < 10% of populations.
(df from technology
independent.
3. Both histograms are unimodal and
MEANS (𝑡)
or df = 𝑛* + 𝑛, − 2) 3. Both populations are Normal.
symmetric*.
1. Data are matched.
1. Think about the design.
Matched pairs
2. Individuals are independent.
2. SRS and 𝑛 < 10% of the population.
(df = 𝑛 − 1)
3. Population of differences is
3. Histogram of differences is unimodal and
Normal.
symmetric*.
1. Data are counts.
1. Are they?
Goodness-of-Fit
2. Data in sample are independent.
2. SRS and 𝑛 < 10% of the population.
(df = cells −1))
3. Sample is sufficiently large.
3. All expected counts ≥ 5.
1. Data are counts.
1. Are they?
DISTRIBUTIONS
Homogeneity
2. Data in groups are independent.
2. SRSs and 𝑛 < 10% of the population.
,
/INDEPENDENCE (𝜒 ) [df = (𝑟 − 1)(𝑐 − 1)]
3. Groups are sufficiently large.
3. All expected counts ≥ 5.
1. Data are counts.
1. Are they?
Independence
2. Data are independent.
2. SRSs and 𝑛 < 10% of the population.
[df = (𝑟 − 1)(𝑐 − 1)]
3. Sample is sufficiently large.
3. All expected counts ≥ 5.
* Less critical as 𝑛 increases. If 𝑛 ≤ 30, then 𝑋 must be approx. normal; If 𝑛 > 30, 𝑋 must not be too skewed.
1.
2.
1.
2.
Notes