STAT 1012: Statistics for Life Science
2013/14 Term 2
Solutions to Practice Problems (Chapter 5)
Problem 1:
(a) Sample covariance is given by s XY
x 247 / 6 41.1667, y 486 / 6 81 . s XY
2
sx
1 n
1 n
( xi x )( yi y )
( xi yi nxy ) .
n 1 i 1
n 1 i 1
1 6
STAT 1012: Statistics for Life Sciences
2013/14 Term 2
Assignment #2 Solutions
Problem 1:
(a) Let A be the event that the 71-year old woman has Alzheimers disease,
B be the event that the 76-year old man has Alzheimers disease, and
C be the event that the
STAT 1012: Statistics for Life Science
2013/14 Term 2
Assignment #3 Solutions
Problem 1:
(a)
2
U Var (U ) Var ( X / 2) Var (Y )
because X and Y are independent
/ 4 / 4 5 / 4
2
X
2
Y
2
X
2
V Var (V ) Var ( X / 3) Var (W / 3)
because X and W are independ
STAT 1012: Statistics for Life Science
2013/14 Term 2
Assignment #2
Due: February 24th, 2014 (Monday)
This assignment covers material from Chapter 2 to 3 of the lecture notes.
Note that the solutions will be available on Feb 26th (Wednesday), as the Mid-t
STAT 1012 Statistics for Life Science
Chapter 6 Estimation
Dr. Philip Lee
2013/14 Term 2
1
Probability vs Statistics
Distribution/
Model
Probability (Ch 2-4)
Statistics (Ch 6-8)
Ch 2-4
Population
Probability model for X
Parameter:
E.g. Population Mean
X
D
STAT 1012 Statistics for Life Sciences
Chapter 3 Discrete Probability Distributions
Dr. Philip Lee
2016/17 Term 1
1
Why Discrete Probability Distribution?
Example: Flip a coin 50 times.
Observe the number of heads.
What are the probabilities of obtaining
STAT 1012 Statistics for Life Sciences
Chapter 4 Continuous Probability Distributions
Dr. Philip Lee
2016/17 Term 1
1
Introduction
(Ch3) Discrete random variable: A random variable which
takes a discrete set of numeric values
(This Chapter) Continuous r
Chapter 2 page 60 (Last Example) - Amendment
Probability in Genetics: ABO Blood Type System
Example: Given that Susan and her father Father
Mother
are of genotype AB and AO respectively.
AO
?
What is the probability that her mother
is of genotype BO?
Susa
STAT 1012 Statistics for Life Science
Chapter 8 Hypothesis Testing:
Two Sample Inference
Dr. Philip Lee
2013/14 Term 2
1
One Sample Tests Covered in Chapter 7
One Sample Z-test
One Sample T-test
One Sample Chi-squared Test
One Sample Z-test for Binomial P
STAT 1012 Statistics for Life Sciences
Syllabus
Dr. Philip Lee
2016/17 Term 1
1
Lecturer and Teaching Assistants
Lecturer:
Email:
Office:
Office Hour:
Telephone No.:
Dr. LEE Pak Kuen, Philip
[email protected]
Lady Shaw Building, Room 116
Monday
STAT 1012 Statistics for Life Science
Chapter 7 Hypothesis Testing:
One Sample Inference
Dr. Philip Lee
2013/14 Term 2
1
Hypothesis Testing
Hypothesis Testing is to make a decision on whether the
parameter of a model is equal to some specific value based
STAT 1012 Statistics for Life Science
Chapter 8 Hypothesis Testing:
Two Sample Inference
Dr. Philip Lee
2013/14 Term 2
1
One Sample Tests Covered in Chapter 7
One Sample Z-test
One Sample T-test
One Sample Chi-squared Test
One Sample Z-test for Binomial P
STAT 1012 Statistics for Life Sciences
Syllabus
Dr. Philip Lee
2013/14 Term 2
1
Lecturer and Teaching Assistants
Lecturer:
Email:
Office:
Office Hour:
Telephone No.:
Teaching Assistant (TA): Mr. LEUNG Sze Him, Issac
Email:
[email protected]
Off
STAT 1012 Statistics for Life Sciences
Chapter 6 Hypothesis Testing:
One Sample
Dr. Philip Lee
2016/17 Term 1
1
Hypothesis Testing ()
Assumption () vs Hypothesis ()
1. An assumption is a statement that is believed to be true.
2. A hypothesis is a statemen
STAT 1012 Statistics for Life Sciences
Chapter 5 Estimation
Dr. Philip Lee
2016/17 Term 1
1
Probability vs Statistics
Distribution/
Model
Probability (Ch 2-4)
Statistics (Ch 5-7)
Population
Data/
Observations
Sample
Ch 2-4
Probability model for X
Paramete
STAT 1012: Statistics for Life Sciences
2016/17 Term 1 Mid-term Review (Chapters 1 to 3)
Date: October 26th 2016 (Wednesday)
Chapter 1 Descriptive Statistics
Types of Variables: Categorical vs Quantitative (Discrete and Continuous) Variables
Shape of a Di
STAT 1012 Statistics for Life Sciences
Chapter 1 Descriptive Statistics
()
Dr. Philip Lee
2015/16 Term 2
1
Introduction
Descriptive statistics (): Use of numeric or
graphic display to describe the main features of a
collection of data
1000 Data Points
x
STAT 1012: Statistics for Life Sciences
2015/16 Term 2
Assignment #2 Solutions
Problem 1:
(a) Let A be the event that the 78-year old man has Alzheimers disease,
B be the event that the 83-year old man has Alzheimers disease, and
C be the event that the 7
STAT 1012: Statistics for Life Sciences
2015/16 Term 2
Assignment #4
Due: April 29th, 2016 (Friday) at 5:00pm
Total Score: 100 points
This assignment covers material from Section 5.4 and 6 of the lecture notes.
You need to show your calculation in details
STAT 1012: Statistics for Life Sciences
2015/16 Term 2
Assignment #2
Due: March 7th, 2016 (Monday) at 6:30pm
Total Score: 100 points
This assignment covers material from Chapter 2 to 3 of the lecture notes.
Please present your answers in 4 significant fig
STAT 1012: Statistics for Life Sciences
2015/16 Term 2
Assignment #3
Due: April 6th, 2016 (Wednesday) at 6:30pm
Total Score: 100 points
This assignment covers material from Chapter 4 to Section 5.4 of the lecture notes.
Problem 1 [21 points]: The blood-gl
STAT 1012: Statistics for Life Sciences
2015-16 Term 2
Assignment #1
Due: February 3rd, 2016 (Wednesday) at 6:30pm
Total Score: 100 points
This assignment covers material from Chapter 1 of the lecture notes.
You need to show your calculation in details or
STAT 1012:Statistics for Life Sciences
2015/16 Term 2
Assignment #1 Solutions
Problem 1:
(a) Mean =(42+44+47+50+51*3+53+57+58+61*2+63+64+67+69+70+74+77+92)/20 = 60.1
Median = (10th smallest and 11th smallest observations)/2 = (58+61)/2=59.5
Mode = 51.0
(b
STAT 1012: Statistics for Life Science
2015/16 Term 2
Solutions to Practice Problems (Chapter 4)
Problem 1: a) Area of the pdf =1 => (5.4-5.2)a=1 => a=5. Hence f(5.25)=a=5. In general, f(x)
is NOT a probability, but instead the height of the pdf curve. Fo
STAT 1012:Statistics for Life Sciences
2016/17 Term 1 Mid-Term Examination Solutions
Problem 1
(a) p=50, np/100=7 => Q2 = Average of 7th and 8th smallest observation = (163+164)/2 = 163.5
p=25, np/100=14(25)/100=3.5 => Q1 = 4th smallest observation = 162
STAT 1012:Statistics for Life Sciences
Mid-Term Formula Sheet (2016/17 Term 1)
Chapter 1 Descriptive Statistics
Sample Mean and Sample Variance: x
1 n
1 n
2
xi x 2
x
,
s
i
n i 1
n 1 i 1
pth percentile:
If np/100 is not an integer, then the pth percentil
STAT 1012: Statistics for Life Science
2013/14 Term 2
Mid-Term Examination Solutions
Problem 1-10: (d), (d), (c), (a), (b), (c), (a), (c), (b), (b)
Problem 11 [16 points]:
(a) Pr(AUB) = Pr(A)+Pr(B)-Pr(AB) = Pr(A) + Pr(B) Pr(A)Pr(B) [as A and B are indepen
STAT 1012 Statistics for Life Science
Chapter 5 Covariance and Correlation
Coefficient
Dr. Philip Lee
2013/14 Term 2
Section 5.6 and 11.7 of Fundamentals of Biostatistics by Bernard Rosner
1
Introduction
Interested in how two quantitative variables are a
STAT 1012: Statistics for Life Sciences
2016/17 Term 1
Solutions to Practice Problems (Chapter 4)
Problem 1: a) Area of the pdf =1 => (5.4-5.2)a=1 => a=5. Hence f(5.25)=a=5. In general, f(x)
is NOT a probability, but instead the height of the pdf curve. F