Probability
(chap. 5)
The probability of an event is the propor8on of 8mes that an
event would occur if we repeated a random trial over and over
again under the same condi8ons.
Probability
To describe a probability, we need to dene an event and the

EEMB 146 Quiz 4
2/13/2015
Name: _
1. You are interested in whether a particular herbicide affects the growth rate of California
poppies. You obtain 20 frogs from a population of interest, and assign them at random to
one of two treatments: (a) 10 frogs ar

EEMB 146 Quiz 3
4/22/2016
Name: _
1. The body weight of all adult finches on an island is normally distributed, with a mean of
50 mg and a variance of 4 mg2.
(a) What is the probability that the weight of a randomly sampled adult finch on the
island will

Paired vs. 2 sample comparisons
Comparing the means of two groups
Hypothesis test: 2-sample t test
Estimation:
Difference between two means
Y1 Y2
Condence interval:
(Y1 Y2 ) SEY Y
1
t
( 2),df
2
Standard error of difference in means
SE Y1 Y2 =
Pooled var

1
EEMB 146 Midterm 4/29/2016
Name: _
1. Jane is studying the effect of drought on California poppies. She has 5 permanent 1 m2 plots
located in poppy habitat. She recorded the number of poppy plants in each plot before and
after the drought. Here are her

1
EEMB 146 Midterm 2/6/2015
1.
Name: _
Researchers studying mice in the Coal Oil Point Reserve are interested in whether
infection with a virus affects the fecundity of female mice. Six randomly-selected
uninfected female mice, and 6 randomly-selected inf

Getting Started With the R Commander
John Fox and Milan Bouchet-Valat
Version 2.2-1 (last modified: 25 August 2015)
1
Introduction
The R Commander (Fox, 2005) provides a graphical user interface (GUI) to the open-source R statistical
computing environment

EEMB 146 Quiz 3
1/30/2015
Name: _
1. Babies born in the U.S. have birth weights that are approximately normally distributed
with mean of 3kg and standard deviation of 0.5 kg.
(a) What is the probability that the weight of a newborn baby in the U.S is betw

Statistical Table B: The standard normal (Z ) distribution
Statistical Table B: The standard normal
(Z) distribution
This table gives probabilities under the right tail of the standard normal distribution.
To determine the probability of sampling a value

EEMB 146 Quiz 2
1/23/2015
Name: _
1. Prof. Z has recently submitted 6 grant proposals. Each grant proposal has a 5% chance of
getting funding. Assume that the probability of any one proposal getting funded does not
influence the chances of any of the othe

T-tests to compare means from 2 groups
Paired vs. 2 sample comparisons
Comparing means when variances
are not equal
Welchs t test
Welch's approximate t-test compares the means of two normally
distributed popula6ons that have unequal variances.
(The pro

Table of formulas:
Population
Number of individuals in population: N
!
! !
mean of a population: =
!
! !
variance of a sample: ! =
Sample
Sample size: n
mean of a sample: =
!
!
! !
!
!
variance of a sample: =
!
!
!
1
!
standard deviation of a sample: =

What to do when the assumptions
are not true
If the sample sizes are large, sometimes the
parametric tests work OK anyway
Transformations
Non-parametric tests
Randomization and resampling
Data transformations
A data transforma+on changes each data poi

EEMB 146 Quiz 4
2/13/2015
Name: _KEY_
1. You are interested in whether a particular herbicide affects the growth rate of California
poppies. You obtain 20 frogs from a population of interest, and assign them at random to
one of two treatments: (a) 10 frog

Table of formulas:
Population
Number of individuals in population: N
!
! !
mean of a population: =
!
! !
variance of a sample: ! =
Sample
Sample size: n
mean of a sample: =
!
!
! !
!
!
variance of a sample: =
!
!
!
1
!
standard deviation of a sample: =

Table of formulas:
Population
Number of individuals in population: N
!
! !
mean of a population: =
!
variance of a population: =
Sample
Sample size: n
mean of a sample: =
!
! !
!
!
!
!
!
variance of a sample: =
!
!
1
!
standard deviation of a sample: =

Steps in Hypothesis Tes.ng
1. State the hypothesis in terms of:
H0: null hypothesis
HA: alterna3ve hypothesis
2. Calculate a test sta3s3c: the quan.ty calculated from the data to test how
compa.ble the data are with the null hypothesis
3. Determin

Infected frog dataset
frog_num
color
1
green
2
green
3
green
4
green
5
green
6
green
7
green
8
green
9
green
10
green
11
green
12
green
13
green
14
green
15
red
16
red
17
red
18
red

EEMB 146
In the computer labs, you will be using R
December 2013
013
em-level studies of terrestrial carbon
ontrasting bacterial metabolism in differatic habitats KATRIN ATTERMEYER, KATRIN
THOMAS HORNICK, SABINE HILT, AND
TER GROSSART
VOL. 94, NO. 12, 2

Frequency distribu/ons & probability distribu/ons
Frequency distribu/on: how o7en each value of a variable occurs in a sample
Probability distribu/on: The distribu/on of a variable in the whole popula/on
0.5
Probability density
25
Frequency
20
15
10
5

Sample means are normally
distributed
(If the variable itself is normally distributed.)
The mean of the sample means is .
The standard deviation of the sample
means is
.
Y =
n
Sample means are normally distributed
If a variable Y in a popula7on is nor

Condi&onal Probability
The condi&onal probability of an event is the probability of that
event occurring, given that a condi&on is met.
Pr[hand washing|female] =
Probability of handwashing,
given the individual is
fe

Do dogs resemble their owners?
Hypothesis testing: an example
Roy, M.M., & Christenfeld, N.J.S. (2004). Do dogs resemble their owners? Psychological Science,
15, 361363
Common wisdom holds that dogs
resemble their owners. Is this true?
41 dog owners appr

One-sample t-test
The one-sample t-test compares the mean of a random sample
from a normal popula2on with the popula2on mean proposed in
a null hypothesis.
Hypotheses for one-sample t-tests
H0 : The mean of the popula2on is 0.
HA: The mean of the po

Sampling from popula.ons
es#mate
The scope of inference refers to the popula.on to which inference
(conclusions) can reasonably be drawn based on the study.
When sampling from a popula.on, we want to nd an ecient way
of obtaining a precise es.mate of

EEMB 146 Midterm 4/29/2016 Name: kEY
1. Jane is studying the effect of drought on California poppies. She has 5 permanent I m2 plots,
randomly located in poppy habitat. She recorded the number of poppy plants in each plot
before and aﬁer the drou ht. Here