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# Lesson 02 class practices

## on Sep 19, 2011

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IBS students 2nd Year, Hanze University of Applied Science

IBS students 2nd Year, Hanze University of Applied Science

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## Lesson 02 class practicesPresentation Transcript

• Statistics 2
Dr. Ning DING
IBS I.007
n.ding@pl.hanze.nl
• Table of Content
Review of Chapter 5
Sampling Distribution
SPSS
In 2003, 1.4 millionstudentstook the SATs. The mean of SAT score is 1026 and the standarddeviation is 209.
Whatproportion of all students had SAT scores of lessthan820?
b. Whatproportion of all students had SAT scores of more than820?
Quiz
Review
Sampling Distribution
SPSS
z = (820-1026)/209 =-0.99
P=0.3389
P=0.5-0.3389=0.1611
P=0.5+0.3389=0.8389
It was foundthat the probability of Americansspendingtheirleisure time fortwo weeks is 0.45; one week is 0.10, and 0.20 forthreeor more weeks. Suppose we have surveyed 20 Americans,
What is the probabilitythat 8 have 2 weeks of vacation of time?
What is the probabilitythatonlyone American has one week of vacation time?
What is the probabilitythat at most 2 of the workers have threeor more weeks of vacation time?
Quiz
Review
Sampling Distribution
SPSS
n=20, p=0.45 P=0.1623
n=20, p=0.10 P=0.2702
n=20, p=0.20 P=0.0115+0.0576+0.1369=0.2060
• Review
Bionomial
Distribution
Poisson
Distribution
Normal
Distribution
Quiz
Review
Sampling Distribution
SPSS
Discrete
within a range
continuous
Discrete
with mean
n!
r ! (n-r) !
Probability of r successes in n trials =
λ: mean
prqn-r
A-3
A-13
A-1
• Chapter 5, No. 5-37 P.270
Review
Quiz
Review
Sampling Distribution
SPSS
1. Visualization is veryuseful !
5-37
Normal Distribution, μ=6.4 σ=2.7
(a). P(4<X<5)=?
Z1=(4-6.4)/2.7=-0.52
P0.52=0.1985
Z2=(5-6.4)/2.7=-0.89
P0.89=0.3133
P(4<X<5)
=0.3133-0.1985
=0.1148
• Chapter 5, No. 5-38 P.270
Review
Quiz
Review
Sampling Distribution
SPSS
2. FromBinomial Distribution to NormalApproximation
5-38
Normalapproximation
N=50 p=0.25
(a). P(x>10)=?
• Review
Bionomial
Distribution
Normal
Distribution
Quiz
Review
Sampling Distribution
SPSS
Discrete
within a range
continuous
Step 1:
Is itallowed?
When n*p>=5 AND n*q>=5
Step 2:
μ =n*p
σ =√n*p*q
Step 3:
Find CCF (ContinuityCorrection Factor)
• Review
Bionomial
Distribution
Normal
Distribution
Quiz
Review
Sampling Distribution
SPSS
Discrete
within a range
continuous
Step 3:
Find CCF (ContinuityCorrection Factor)
X<3
X=<3
X>3
X>=3
Discrete:
1 2 3 4 5 6 7 8
CCF X>3.5
CCF X>2.5
CCF X<2.5
CCF X<3.5
Continuous:
1 2 3 4 5 6 7 8
• Chapter 5, No. 5-38 P.270
Review
Quiz
Review
Sampling Distribution
SPSS
2. FromBinomial Distribution to NormalApproximation
5-38
Normalapproximation
N=50 p=0.25
(a). P(x>10)=?
Step 1:
n*p=50*0.25=12.5 >5
AND n*q=50*0.75=37.5 >5
Yes, it is allowed.
Step 2:
n*p=50*0.25=12.5 =μ
σ=√n*p*q= √50*0.25*0.75=3.062
Step 3:
CCF X=10.5
P(x>10.5)=?
z=(10.5-12.5)/3.062 =0.65
• Chapter 5, No. 5-38 P.270
Review
Quiz
Review
Sampling Distribution
SPSS
2. FromBinomial Distribution to NormalApproximation
5-38
Normalapproximation
N=50 p=0.25
(a). P(x>10)=?
Step 3:
CCF X=10.5
P(x>10.5)=?
z=(10.5-12.5)/3.062 =0.65
Step 4: Visualization
P0.65=0.2422
P(x>10)
=0.2422+0.5
=0.7422
• Chapter 5, No. 5-39 P.270
Review
Quiz
Review
Sampling Distribution
SPSS
3. If P is known, butcannotbefound in the table, it is allowed to use the closestone.
5-39
Normal Distribution σ=5.0 X=21 P=0.14
(a). μ=?
(b). X1?  P(X<X1)= 4%
Visualization
Pz=0.50-0.14=0.36  z=1.08
(21-μ)/5.0=1.08
μ=15.6
Pz=0.5-0.04=0.46
 z=1.75
(X1-15.6)/5.0=-1.75
X1=6.85
• Chapter 5, No. 5-41 P.270
Review
5-41
μ=100, P(X<115)=0.9
(a). σ=?
Quiz
Review
Sampling Distribution
SPSS
Visualization
z =1.28
z =1.28=(115-100)/σσ=11.72
• Chapter 5, No. 5-41 P.270
Review
5-41
μ=100, P(X<115)=0.9
(a). σ=11.72
(b). Stock at least ___?
Quiz
Review
Sampling Distribution
SPSS
Visualization
(X-100)11.72=1.645 
z =1.645 
X=119.28
Therefore, we’dbetter stock at least 120 tubes.
• The Normal Distribution
Molly earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What proportion of students had a higher score than Molly?
(A) 0.10 (B) 0.18 (C) 0.50 (D) 0.82 (E) 0.90
Group Discussion
Quiz
Review
Sampling Distribution
SPSS
• Self-Practice
Chapter 5, No. 5-37 P.270
Quiz
Review
Sampling Distribution
SPSS
Given that a random variable, X, has a normal distribution with mean 6.4 and standard deviation 2.7, find
Q1. P (4.0<x<5.0)
Q2. P(x>20)
Q3. P(x<7.2)
Q4. P((x<3.0) or (x>9.0))
• Chapter 5, No. 5-37 P.270
Quiz
Review
Sampling Distribution
SPSS
Given that a random variable, X, has a normal distribution with mean 6.4 and standard deviation 2.7, find
Q1. P (4.0<x<5.0)
Q2. P(x>20)
Q3. P(x<7.2)
Q4. P((x<3.0) or (x>9.0))
Self-Practice
• Sampling and Sampling Distribution
Quiz
Review
Sampling Distribution
SPSS
Population
Sample
= all items chosen for study
= a portion chosen from the population
Parameter
Statistic
 Greek or capital letters
 Lowercase Roman letters
• Standard Error
Population Range=80~240
Quiz
Review
Sampling Distribution
SPSS
µ = 100
σ = 25
=95
Sample Range=90~120
=106
=101
Standard Error of mean
Standard Deviation of population
____
• Standard Error
Quiz
Review
Sampling Distribution
SPSS
Sample size
Dispersion of means
Standard Error
• The Normal Distribution
SPSS Tip: Descriptive Statistics
Blackboard – Inductive Statsitics STA2—SPSS--Week 2 Creating Graphs.sav
• SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
Type data into SPSS
- Gender
- Age
- Satisfaction with STA2
1 2 3 4 5
Hate it -------- Not like it --------- So so------------Like it-----Addicted to it
• SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
Type data into SPSS
- Gender
- Age
- Satisfactionwith STA2
2. Click on “Values” to define variables
e.g. 0=male; 1=female
1 2 3 4 5
Hate it -------- Not like it --------- So so------------Like it-----Addicted to it
1. Use the Variable View Tab
• SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
Type data into SPSS
- Gender
- Age
- Satisfaction with STA2
4. Input data intoeach column
3. Use the Data View Tab
• SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
Type data into SPSS
- Gender
- Age
- Satisfaction with STA2
5. Don’tforget to choose the measurement level.
* . Youcanedit the variables again.
• 6. Analyze—descriptivestatistics--Descriptive
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
• SPSS Tip: Descriptive Statistics
Nowyougetit!
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
• 7. Analyze—descriptivestatistics--Frequencies
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
• 8. Choose the variableyouneed to analyze
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution