2.1: Sampling from a Finite Population
Review
Population: entire collection of observational units
Sample: subset of population
Parameter: numerical summary for population
(unknown)
Statistic: numerical summary for sample (known)
Definitions
Represen
1.4: What Impacts Strength of Evidence
z=
statisticmean
standard error
1. Difference between the statistic and mean
Further away statistic is from the mean => larger
z-score (in absolute value) => smaller p-value
2. Sample size
Larger sample size => les
2.2 Inference for a Single Quantitative Variable
Categorical variables => make inferences to
population proportion (
Quantitative variable => make inferences to
population mean (
Definitions
Median: middle value of the data
o 9, 5, 7, 2, 8
2, 5, 7,
3.3: Confidence Intervals for a Single Mean
t=
x
s / n
Confidence Interval:
x Multiplier
Statistic Multiplier Standard Error
s
n
Valid for symmetric (bell-shaped) distribution
Must have sample size of at least 20
Example: A sample of 102 Honda Civics
3.1 and 3.4 Confidence Intervals
Example: Kissing Right?
A study showed that 80 out of 124 couples leaned their heads to
the right while kissing. Is the direction couples lean in actually
random?
H 0 : =0.50
H A : 0.50
^p=
p
80
=0.65
124
-value
0.0012
In
1.3: Alternative Measure of Strength of Evidence
Example: Heart Transplant Operations
15% of patients who received heart transplant operations
nationally have died. After 8 out of 10 people who
received heart transplants died at St. Georges hospital,
rese
4.1: Association and Confounding
Explanatory variable: variable that is explaining the
change
Response variable: variable that is being changed
o e.g. smoking (explanatory variable) => lung
cancer (response variable)
o e.g. high school GPAs (explanatory
3.2: Confidence Intervals for a Proportion
2<
2
p^
<2
( 1 )
n
( 1 )
(1 )
< ^p <2
n
n
^p 2
^p +2
^p2
( 1 )
( 1 )
< < ^p +2
n
n
( 1 )
( 1 )
> > ^p2
n
n
( 1 )
( 1 )
< < ^p +2
n
n
Issue: Want by itself but is in the standard
error on each side of
2.3 Errors and Significance
Type I error: Rejecting the null hypothesis when in
reality the null hypothesis is true
Type II error: Failing to reject the null hypothesis when
in reality the null hypothesis is false
Reality
is true
Type I error
(false alarm
1.2: Measuring the Strength of Evidence
Binary variable: categorical variable with only 2
outcomes (e.g. gender, flipping a coin, made/missed
free throw)
Symbols
e.g.
is the long run proportion (parameter)
=
1
3
is the long run probability of winning in