1) Two different scientists are interested in
the weights of male bumblebees. Each one
takes a random sample from the same
population and uses it to estimate the mean
and the 95% confidence interval of the
mean. These are their results:
Scientist A
Scient

Estimating binomial
parameters
What is the sex ratio at
birth of red deer?
Alternative notation for estimators
is the estimator of
Xis the estimator of
X
etc.
That is, the estimator is
represented by the symbol for
the parameter with a carat on
top.
is
p

The right term gives the
probability of exactly x
successes and nx failures
PX x
n x
n x
p 1 p
x
The left term gives the
number of possible
combinations of x successes
and nx failures.
The product of the two terms gives
the total probability of having

Statistics: The method of saying
something about the real world
based on observations influenced by
randomness
Two main areas:
1.Using data to estimate
unknown parameters.
2.Using data to test hypotheses
about unknown parameters.
Examples of parameters to

Hypothesis testing,
continued
Review of steps in hypothesis
testing
1. Specify null and alternative
hypotheses.
2. Select a significance level
(acceptable Type I error).
3. Choose a test statistic: a single value
to be calculated from data.
4. Collect da

Definition of the variance of a
discrete random variable:
x
x
2
PX x
The variance expresses our uncertainty
about the value taken by a random
variable
Low variance, high
certainty
High variance, low
certainty
Probability
0
25
Mean = 12
Variance = 4
0
25

The normal distribution
The normal distribution includes
all real numbers, but most
observations are bunched around
a particular location.
Normal
PDF
Probabilit
y density
X
Probability density function of a
normal random variable
x
1
f x
e
2
2
2 2
x

Bio 415: Biometry
Lecturer: Stephen Pratt
TAs: Heather Kropp, Rick
Simpson
1. What statistical software have you
used, if any?
A. R
B. SPSS
C. JMP
D. Minitab
E. Excel
F. Other
G. None
2. How much computer programming
experience do you have? (On a scale
of

Discrete random
variables;
The binomial
distribution
Motivating question (sex ratio
example)
Of 12 deer
offspring:
10 are males
If sex ratios are equal, should we be
surprised to see these data?
Answer comes from probability
theory.
The number of males