STAT:3510 (22S:101) BIOSTATISTICS
Chapter 2 Introduction to Probability
Recall Inductive Inference: Sample Population.
Inductive inference is uncertain.
Major role of statistics: to recognize and quantify the uncertainty in inductive
inference.
Probabilit
STAT:3510 (22S:101) BIOSTATISTICS
Chapter 1 Introduction to Data Analysis
Anticipated Learning Outcomes from the Course
At the end of the semester, a student is expected to
have knowledge on basic statistical methods commonly used in the biological
scien
STAT:3510 (22S:101) BIOSTATISTICS
Chapter 3 Probability Distributions
Discrete Random Variables
For a given sample space S of some experiment, a random variable is a rule
(function) that maps each outcome in S to a numerical value. A random variable
is a
Discussion 10
22S:101:BBB
Biostatistics
1. Age and systolic blood pressure (SBP) among 5 adult women:
Age
SBP
27
106
41
139
32
122
51
144
59
157
Suppose a least square regression line of SBP vs. Age is already
obtained:
SBP = 72.3 + 1.46 Age
(1)Compute th
Discussion 9
22S:101:BBB
Biostatistics
1. Based on a sample of size 20, a frequentist provides the confidence interval
[134, 140] for the average triglyceride level of a population of cardiac
patients. Use this information to compute P( > 139 | data).
2.
Discussion 10
22S:101:BBB
Biostatistics
1. Scatterplots of y vs. x, x vs. z, z vs. y are shown below. What can you
conclude about the relations among them?
2. Suppose we have following data:
3
1
Can you calculate the slope and intercept
regression line
?
Discussion 8
22S:101:BBB
Biostatistics
1. In a random sample of 100 male and 125 female Iowa
residents, the average LDL cholesterol level for the males
are 180 (mg/dL) with standard deviation 30, while the
average for the females are 170 with standard dev
Discussion 7
22S:101:BBB
Biostatistics
1. Suppose the frequentist p-value for a test of H:
vs. A:
is 0.06. If we use independent uniform
priors on and , what Bayesian conclusion can we make?
2. Denote
= the odds ratio of heavy over light smoking
and simil
Discussion 5
22S:101:BBB
Biostatistics
1. Let denote the proportion of all asthma patients that
can benefit from a certain new medicine.
(1)If has a uniform[0,1] prior, compute the 95% credible
interval for .
(2)If has a Beta(21,16) prior, obtain the 95%
Discussion 6
22S:101:BBB
Biostatistics
1. Let denote the proportion of all depression patients that
can benefit from a new medicine, and the proportion of
all depression patients that can benefit from taking a
placebo. Assume , have independent uniform[0,
Discussion 4
22S:101:BBB
Biostatistics
1. A marksman blindfolds himself and thinks that on average he
will hit the target 4 out of 5 times.
(1) If he fires 4 shots, whats the probability of more than 2
misses if he is right about his hitting percentage?
(
Discussion 3
22S:101:BBB
Biostatistics
1. A room contains 6 male and 4 female students. Students leave the room one-ata-time, in random order. Let N denote the number of male students who are
preceded immediately by one female student (for example, in the
Discussion 2
22S:101:BBB
Biostatistics
1. A doctor is studying the relationship between blood pressure and heartbeat
abnormalities in her patients. She tests a random sample of her patients and notes
their blood pressures (high, low, or normal) and their
Discussion 1
22S:101:BBB
Biostatistics
1. For a fair 6-sided die,
(1) Whats the probability of getting an even number in one toss?
(2) Whats the probability of getting 1 or 2 in one toss?
(3) Are the two events described in (1), (2) mutually exclusive? In
22S:101
QUIZ #3
Due Friday 16 Nov
Print name_
1)
Suppose your prior distribution for = the success rate of a drug is beta(12, 4). You observe
15 successes and 10 failures in an experiment. Use the appropriate table on the back page of
this exam to determi
22S:101
Midterm#2
1 Nov 2012
Print name_
1)
Suppose your prior distribution for = the success rate of a drug is beta(12, 4). You observe
15 successes and 10 failures in an experiment. Use the appropriate table on the back page of
this exam to determine an
S:101 Midt #1
practice
print name_sec_
1) Which data set corresponds to the histogram shown.
10
20
30
a) 12, 12, 32, 55, 56
40
50
60
b) 11, 33, 36, 36, 47
c) 12, 24, 36, 41, 58
c) 15, 21, 32, 39, 55
d) 15, 22, 35, 55, 59
2) Find the SD of the data set 102
S101 Homework
assignment must have a due date to be official
Assignment 1
1)
Suppose 15% of adult Iowans suffer from hypertension. Find the probability that
at least one of 8 randomly chosen Iowans suffers from hypertension.
2)
One patient is randomly sel
STAT:3510 (22S:101) CCC
First Name:
Discussion Section Number:
Biostatistics
Quiz 5 (10 pts)
Last Name:
1. Consider the chi-square distribution with 3 degrees of freedom.
a) What proportion of the area under the curve lies to the right of 2 = 6.25? (2 pts
STAT:3510 (22S:101) CCC
First Name:
Discussion Section Number:
Biostatistics
Quiz 5 (10 pts)
Last Name:
1. Consider the chi-square distribution with 5 degrees of freedom.
a) What proportion of the area under the curve lies to the right of 2 = 11.07? (2 pt
STAT:3510 (22S:101) CCC
First Name:
Discussion Section Number:
Biostatistics
Quiz 5 (10 pts)
Last Name:
1. Consider the chi-square distribution with 3 degrees of freedom.
a) What proportion of the area under the curve lies to the right of 2 = 7.81? (2 pts
STAT:3510 (22S:101) CCC
First Name:
Discussion Section Number:
Biostatistics
Quiz 4 (10 pts)
Last Name:
1. Consider the t distribution with 15 degrees of freedom.
a) What proportion of the area under the curve lies to the right of t = 1.753? What proporti
STAT:3510 (22S:101) CCC
First Name:
Discussion Section Number:
Biostatistics
Quiz 4 (10 pts)
Last Name:
1. Consider the t distribution with 9 degrees of freedom.
a) What proportion of the area under the curve lies to the right of t = 4.781? What proportio
STAT:3510 (22S:101) CCC
First Name:
Discussion Section Number:
Biostatistics
Quiz 4 (10 pts)
Last Name:
1. Consider the t distribution with 6 degrees of freedom.
a) What proportion of the area under the curve lies to the right of t = 3.707? What proportio
22S:101:CCC
First Name:
Discussion Section Number:
Biostatistics
Practice Midterm-I
Last Name:
This exam contains 17 multiple choice questions (please circle only one choice for each
question) each worth 3 points, and 1 non-multiple choice question worth