Lesson 02 class practices
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description
IBS students 2nd Year, Hanze University of Applied Science
Transcript of Lesson 02 class practices
Table of Content
1. Review of Chapter 5
2. Sampling Distribution
3. SPSS
Quiz Answer
In 2003, 1.4 million students took the SATs. The mean of SAT score is 1026 and the standard deviation is 209.
a. What proportion of all students had SAT scores of less than 820?
b. What proportion of all students had SAT scores of more than 820?
z = (820-1026)/209 =-0.99
P=0.3389
P=0.5-0.3389=0.1611
P=0.5+0.3389=0.8389
Quiz
Review
Sampling Distribution
SPSS
Quiz Answer
It was found that the probability of Americans spending their leisure time for two weeks is 0.45; one week is 0.10, and 0.20 for three or more weeks. Suppose we have surveyed 20 Americans,
a. What is the probability that 8 have 2 weeks of vacation of time?
b. What is the probability that only one American has one week of vacation time?
c. What is the probability that at most 2 of the workers have three or more weeks of vacation time?
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
Quiz
Review
Sampling Distribution
SPSS
Review
BionomialDistribution
Poisson Distribution
Discretewithin a range
Normal Distribution
continuousDiscretewith mean
Probability of r successes in n trials =
n!
r ! (n-r) !
pr qn-rλ: mean
A-3 A-13 A-1
Quiz
Review
Sampling Distribution
SPSS
Review
1. Visualization is very useful !
5-37 Normal Distribution, μ=6.4 σ=2.7
(a). P(4<X<5)=?
Chapter 5, No. 5-37 P.270
Z2=(5-6.4)/2.7=-0.89P0.89=0.3133
Z1=(4-6.4)/2.7=-0.52P0.52=0.1985
P(4<X<5)=0.3133-0.1985=0.1148
Quiz
Review
Sampling Distribution
SPSS
Review
2. From Binomial Distribution to Normal Approximation
5-38
Chapter 5, No. 5-38 P.270
Normal approximation
N=50 p=0.25
(a). P(x>10)=?
Quiz
Review
Sampling Distribution
SPSS
Review
BionomialDistribution
Discretewithin a range
Normal Distribution
continuous
Step 1: Is it allowed?When n*p>=5 AND n*q>=5
Step 2: μ =n*pσ =√n*p*q
Step 3: Find CCF (Continuity Correction Factor)
Quiz
Review
Sampling Distribution
SPSS
Review
BionomialDistribution
Discretewithin a range
Normal Distribution
continuous
Step 3: Find CCF (Continuity Correction Factor)
Discrete:
Continuous:
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
X>3
CCF X>3.5
X>=3
CCF X>2.5
X<3
CCF X<2.5
X=<3
CCF X<3.5
Quiz
Review
Sampling Distribution
SPSS
Review
2. From Binomial Distribution to Normal Approximation
5-38
Chapter 5, No. 5-38 P.270
Normal approximation
N=50 p=0.25
(a). P(x>10)=?
Step 1: n*p=50*0.25=12.5 >5AND n*q=50*0.75=37.5 >5 Yes, it is allowed.
Step 2: n*p=50*0.25=12.5 =μσ=√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
Quiz
Review
Sampling Distribution
SPSS
Review
2. From Binomial Distribution to Normal Approximation
5-38
Chapter 5, No. 5-38 P.270
Normal approximation
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
P0.65=0.2422
P(x>10)=0.2422+0.5=0.7422
Step 4: Visualization
Quiz
Review
Sampling Distribution
SPSS
Review
3. If P is known, but cannot be found in the table, it is allowed to use the closest one.
5-39
Chapter 5, No. 5-39 P.270
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
(X1-15.6)/5.0=-1.75X1=6.85
Pz=0.5-0.04=0.46 z=1.75
Quiz
Review
Sampling Distribution
SPSS
Review
5-41
Chapter 5, No. 5-41 P.270
μ=100, P(X<115)=0.9(a). σ=?
Visualization
z =1.28
z =1.28=(115-100)/σσ=11.72
Quiz
Review
Sampling Distribution
SPSS
Review
5-41
Chapter 5, No. 5-41 P.270
μ=100, P(X<115)=0.9(a). σ=11.72
(b). Stock at least ___?
Visualization
(X-100)11.72=1.645 z =1.645 X=119.28
Therefore, we’d better stock at least 120 tubes.
Quiz
Review
Sampling Distribution
SPSS
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
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))
Quiz
Review
Sampling Distribution
SPSS
Chapter 5, No. 5-37 P.270
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
Quiz
Review
Sampling Distribution
SPSS
Sampling and Sampling Distribution
Population
= all items chosen for study
Sample
= a portion chosen from the population
Parameter Statistic
Greek or capital letters Lowercase Roman letters
Quiz
Review
Sampling Distribution
SPSS
Standard Error
µ = 100σ = 25
=95
=106
=101
Population Range=80~240
Sample Range=90~120
Standard Error of mean
Standard Deviation of population____
Quiz
Review
Sampling Distribution
SPSS
Standard Error
Sample size
Dispersion of means
Standard Error
Quiz
Review
Sampling Distribution
SPSS
The Normal DistributionSPSS Tip: Descriptive Statistics
The data can be downloaded from:
Blackboard – Inductive Statsitics STA2—SPSS--Week 2 Creating Graphs.sav
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
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
More about Sampling
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
2. Click on “Values” to define variables
e.g. 0=male; 1=female
1. Use the Variable View Tab
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
Type data into SPSS- Gender- Age- Satisfaction with STA2
4. Input data into each column
3. Use the Data View Tab
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
Type data into SPSS- Gender- Age- Satisfaction with STA2
5. Don’t forget to choose the measurement level.
* . You can edit the variables again.
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
SPSS Tip: Descriptive Statistics6. Analyze—descriptive statistics--Descriptive
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
Now you get it!
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
7. Analyze—descriptive statistics--Frequencies
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
8. Choose the variable you need to analyze
9. Click “Statistcs” to choose more
SPSS Tip: Descriptive Statistics
Quiz
Sampling
Random Sampling
Experiment Design
Sampling Distribution
More about Sampling
Now you get it!
Summary
1. Review of Chapter 5
2. Sampling Distribution
3. SPSS
