STAT 1012 Statistics for Life Science
Tutorial 7 - Confidence Intervals
1) Confidence Interval: One-sample-Normal-Mean-Known Variance
Example 1
Given that height of a certain class of students are normally distributed with unknown mean but known variance
STAT 1012: Statistics for Life Science
2012/13 Term 1
Review of Chapter 2 to 4
Date: October 24th 2012 (Wednesday)
Brief Summary of Chapter 2 to 4
Chapter 2
Descriptive Statistics
Types of Data: Categorical vs Quantitative (Discrete and Continuous) Data
S
STAT 1012: Statistics for Life Science
2012/13 Term 1
Practice Exercise for Chapter 6
* The solutions are attached at the bottom of this document.
Problem 1: Suppose a clinical trial is conducted to test the efficacy of a new drug,
spectinomycin (an amino
STAT 1012: Statistics for Life Science
2012/13 Term 1
Practice Exercise for Chapter 7
Problem 1 (Multiple Choice): The p-value for testing H0: =100 vs H1: 100 is 0.001. This
indicates that
(a) There is strong evidence that =100.
(b) There is strong eviden
STAT 1012: Statistics for Life Science
2012/13 Term 1
Practice Exercise for Chapter 5
* The solutions are attached at the bottom of this document.
* Note that when we use the Normal table, say to calculate the value for (1.234), we can
round up the percen
STAT 1012 Statistics for Life Science
Tutorial 8 - Hypothesis Testing (One-sample)
Exercises:
(known ) and a walkthrough
Example 1
A successful commercial advertisement should increase the sales volume. We measure the monthly sales
volume increase of a mo
STAT 1012 Statistics for Life Science
Tutorial 8 - Hypothesis Testing (One-sample)
Example 1
Null hypothesis ( ): =0
Alternative hypothesis ( ):
>0
a)
1st Method: Using table
=
Since
= 1.78885 > 1.645 =
Therefore, null hypothesis is rejected.
OR
2nd Metho
STAT 1012 Statistics for Life Science
Tutorial 6 - Continuous Random Variables
Example 1
First of all, find Cov(X,Y)
We are given Corr(X,Y) = 0.25
Cov(X,Y) = 0.25( )( ) = 1.5
0.25
a) Var(X-2Y) = Var(X) + Var(2Y) 2Cov(X,2Y) = Var(X) +
Var(Y) 2(2)Cov(X,Y) =
STAT 1012 Statistics for Life Science
Tutorial 5 - Continuous Random Variables
1) Normal Distribution
Example 1
(a) Find Pr(Z>1) where Z~N(0,1)
(b) Find Pr(Z<-1)
(c) Find Pr(X<-1) where X~N(4,4)
Example 2
On May 5, in a certain city, temperatures have bee
STAT 1012 Statistics for Life Science
Tutorial 5 - Continuous Random Variables
Note that there is no difference between
or
in continuous random variables.
Example 1
a) Pr(Z>1) = 1-Pr(Z<1) = 1- 0.8413 = 0.1587
b) Pr(Z<-1) = Pr(Z>1) (by symmetry of normal d
STAT 1012 Statistics for Life Science
Tutorial 5 - Continuous Random Variables
1) Normal Distribution
Example 1
(a) Find Pr(Z>1) where Z~N(0,1)
(b) Find Pr(Z<-1)
(c) Find Pr(X<-1) where X~N(4,4)
Example 2
On May 5, in a certain city, temperatures have bee
STAT 1012 Statistics for Life Science
Tutorial 4 - Discrete Random Variables
1) Random variables
Example 1
State whether the random variables are discrete or continuous.
(a) A coin is tossed ten times. The random variable X is the number of tails that are
STAT 1012 Statistics for Life Science
Tutorial 4 - Discrete Random Variables
Random variables
Example 1
State whether the random variables are discrete or continuous.
(a) A coin is tossed ten times. The random variable X is the number of tails that are no
STAT 1012 Statistics for Life Science
Tutorial 3 - Conditional Probability and Bayes Theorem
1) (Review) Conditional Probability:
We define P(B|A), the conditional probability of B happens given that we know A happens =
P(B|A) = P(B A)/P(A)
Note:
1: The s
STAT 1012 Statistics for Life Science
Tutorial 1 - Descriptive Statistics
1) Types of Data:
Categorical:
Quantitative:
Variables which only
identify which category does
an observation belong to.
No math. operations (e.g. + * / < >) can be applied on
them
STAT 1012 Statistics for Life Science
Tutorial 2 - (Cont.) Descriptive Stat. and Probability
1) (Cont.) Measure of Spread:
Variance
1.
,where
Standard
Deviation
OR
Coefficient
of Variation
Takes into
account of
all
observations
deviations
from mean.
Sam
STAT 1012 Statistics for Life Science
Tutorial 3 - (Cont.) Descriptive Stat. and Probability
Example 1.1:
Pr(A|B) = Pr(A
B) / Pr(B) = Pr( female and French) / Pr(French) = (10/100)/(60/100) = 1/6
Example 4.1:
Let A denote the event of a dot is sent.
Let B
STAT 1012 Statistics for Life Science
Tutorial 1 - Descriptive Statistics
1) Types of Data:
Categorical:
Quantitative:
Variables which only
identify which category does
an observation belong to.
No math. operations (e.g. + * / < >) can be applied on
them
STAT 1012 Statistics for Life Science
Tutorial 2 - (Cont.) Descriptive Stat. and Probability
Example 1.1:
If Variance = 0,
1n
( X i X )2 0
n 1 i 1
X 1 X 0, X 2 X 0,., X n X 0 , which means that for every i, we have the same value = X
If all observations
STAT 1012: Statistics for Life Science
2012/13 Term 1
Practice Exercise for Chapter 8
Problem 1: Which of the following is true if the significance level of a test increases from
0.01 to 0.05?
(i)
Probability of Type II error increases
(ii)
Length of conf
STAT 1012: Statistics for Life Science
2012/13 Term 1
Practice Exercise for Chapter 5a
Problem 1: Suppose that X and Y are independent. Show that Var(X-Y)=Var(X)+Var(Y).
Some of you may have a misperception that Var(X-Y)=Var(X)-Var(Y). This not true becau
STAT 1012: Statistics for Life Science
Practice Exercise - Chapter 2
Solutions will be posted to the course website on October 10, 2012 (Wednesday)
Multiple Choice Questions:
Problem 1: If an extreme outlier exists in the data set, which of the following
Example to Rethink about Section 6.1
Suppose that a sample of 6 data points are observed from
N(,9) [our population!] with unknown population mean
but known population variance 2=9.
The 6 sample points are ( x1, x2 , x3 , x4 , x5 , x6 ) (6, 8, 10, 10,1
Page 61 of Chapter 2
Stem-and-leaf Plot
10th observation 3,245
11th observation 3,248
Median = 3200+(45+48/2)
=3,246.5
Each data point is converted into stem and leaf.
E.g., 2069 (stem: 20; leaf: 69)
Table 2.1 Sample birthweights (g) of
live-born infant
Example on Null and Alternative Hypothesis
Example: A new drug was made to increase the response rate of the
nervous system. For rats without injecting the drug, the mean
response time is 1.2 seconds. Of the 100 rats with the drug injected,
the average re
Chapter 2
Suppose that there are 1,000 students in a class. Each of them
flip the same coin 10 times and record the number of heads
each students observed. Below is the frequency table of the
number of heads observed by each student:
Question: Is the coin