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Lesson 02 class practices

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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 practices Lesson 02 class practices Presentation Transcript

    • Statistics 2
      Dr. Ning DING
      IBS I.007
      n.ding@pl.hanze.nl
    • Table of Content
      Review of Chapter 5
      Sampling Distribution
      SPSS
    • Quiz Answer
      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
    • Quiz Answer
      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
      The data can be downloaded from:
      Blackboard – Inductive Statsitics STA2—SPSS--Week 2 Creating Graphs.sav
    • 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
    • SPSS Tip: Descriptive Statistics
      Quiz
      Sampling
      Random Sampling
      Experiment Design
      Sampling Distribution
      More about Sampling
      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
      More about Sampling
      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
      More about Sampling
      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
      More about Sampling
    • SPSS Tip: Descriptive Statistics
      Nowyougetit!
      Quiz
      Sampling
      Random Sampling
      Experiment Design
      Sampling Distribution
      More about Sampling
    • 7. Analyze—descriptivestatistics--Frequencies
      SPSS Tip: Descriptive Statistics
      Quiz
      Sampling
      Random Sampling
      Experiment Design
      Sampling Distribution
      More about Sampling
    • 8. Choose the variableyouneed to analyze
      SPSS Tip: Descriptive Statistics
      Quiz
      Sampling
      Random Sampling
      Experiment Design
      Sampling Distribution
      More about Sampling
      9. Click “Statistcs” to choose more
    • SPSS Tip: Descriptive Statistics
      Quiz
      Sampling
      Random Sampling
      Experiment Design
      Sampling Distribution
      More about Sampling
      Nowyougetit!
    • Summary
      Review of Chapter 5
      Sampling Distribution
      SPSS