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Lesson 02 class practices

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Lesson 02 class practices

1. 1. Statistics 2<br />Dr. Ning DING<br />IBS I.007<br />n.ding@pl.hanze.nl<br />
2. 2. Table of Content<br />Review of Chapter 5<br />Sampling Distribution<br />SPSS<br />
3. 3. Quiz Answer<br />In 2003, 1.4 millionstudentstook the SATs. The mean of SAT score is 1026 and the standarddeviation is 209. <br />Whatproportion of all students had SAT scores of lessthan820?<br />b. Whatproportion of all students had SAT scores of more than820?<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />z = (820-1026)/209 =-0.99<br />P=0.3389<br />P=0.5-0.3389=0.1611<br />P=0.5+0.3389=0.8389<br />
4. 4. Quiz Answer<br />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, <br />What is the probabilitythat 8 have 2 weeks of vacation of time?<br />What is the probabilitythatonlyone American has one week of vacation time?<br />What is the probabilitythat at most 2 of the workers have threeor more weeks of vacation time?<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />n=20, p=0.45 P=0.1623<br />n=20, p=0.10 P=0.2702<br />n=20, p=0.20 P=0.0115+0.0576+0.1369=0.2060<br />
5. 5. Review<br />Bionomial<br />Distribution<br />Poisson<br />Distribution<br />Normal<br />Distribution<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Discrete<br />within a range<br />continuous<br />Discrete<br />with mean<br />n!<br />r ! (n-r) !<br />Probability of r successes in n trials =<br />λ: mean<br />prqn-r<br />A-3<br />A-13<br />A-1<br />
6. 6. Chapter 5, No. 5-37 P.270<br />Review<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />1. Visualization is veryuseful !<br />5-37 <br />Normal Distribution, μ=6.4 σ=2.7<br />(a). P(4<X<5)=?<br />Z1=(4-6.4)/2.7=-0.52<br />P0.52=0.1985<br />Z2=(5-6.4)/2.7=-0.89<br />P0.89=0.3133<br />P(4<X<5)<br />=0.3133-0.1985<br />=0.1148<br />
7. 7. Chapter 5, No. 5-38 P.270<br />Review<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />2. FromBinomial Distribution to NormalApproximation<br />5-38 <br />Normalapproximation<br />N=50 p=0.25<br />(a). P(x>10)=?<br />
8. 8. Review<br />Bionomial<br />Distribution<br />Normal<br />Distribution<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Discrete<br />within a range<br />continuous<br />Step 1: <br />Is itallowed?<br />When n*p>=5 AND n*q>=5<br />Step 2: <br />μ =n*p<br />σ =√n*p*q<br />Step 3: <br />Find CCF (ContinuityCorrection Factor)<br />
9. 9. Review<br />Bionomial<br />Distribution<br />Normal<br />Distribution<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Discrete<br />within a range<br />continuous<br />Step 3: <br />Find CCF (ContinuityCorrection Factor)<br />X<3<br />X=<3<br />X>3<br />X>=3<br />Discrete: <br /> 1 2 3 4 5 6 7 8<br />CCF X>3.5<br />CCF X>2.5<br />CCF X<2.5<br />CCF X<3.5<br />Continuous: <br /> 1 2 3 4 5 6 7 8<br />
10. 10. Chapter 5, No. 5-38 P.270<br />Review<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />2. FromBinomial Distribution to NormalApproximation<br />5-38 <br />Normalapproximation<br />N=50 p=0.25<br />(a). P(x>10)=?<br />Step 1: <br />n*p=50*0.25=12.5 >5<br />AND n*q=50*0.75=37.5 >5<br />Yes, it is allowed. <br />Step 2: <br />n*p=50*0.25=12.5 =μ<br />σ=√n*p*q= √50*0.25*0.75=3.062<br />Step 3: <br />CCF X=10.5<br />P(x>10.5)=?<br />z=(10.5-12.5)/3.062 =0.65<br />
11. 11. Chapter 5, No. 5-38 P.270<br />Review<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />2. FromBinomial Distribution to NormalApproximation<br />5-38 <br />Normalapproximation<br />N=50 p=0.25<br />(a). P(x>10)=?<br />Step 3: <br />CCF X=10.5<br />P(x>10.5)=?<br />z=(10.5-12.5)/3.062 =0.65<br />Step 4: Visualization<br />P0.65=0.2422<br />P(x>10)<br />=0.2422+0.5<br />=0.7422<br />
12. 12. Chapter 5, No. 5-39 P.270<br />Review<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />3. If P is known, butcannotbefound in the table, it is allowed to use the closestone. <br />5-39 <br />Normal Distribution σ=5.0 X=21 P=0.14<br />(a). μ=?<br />(b). X1?  P(X<X1)= 4%<br />Visualization<br />Pz=0.50-0.14=0.36  z=1.08<br />(21-μ)/5.0=1.08<br />μ=15.6<br />Pz=0.5-0.04=0.46<br /> z=1.75<br />(X1-15.6)/5.0=-1.75<br />X1=6.85<br />
13. 13. Chapter 5, No. 5-41 P.270<br />Review<br />5-41 <br />μ=100, P(X<115)=0.9<br />(a). σ=?<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Visualization<br />z =1.28<br />z =1.28=(115-100)/σσ=11.72<br />
14. 14. Chapter 5, No. 5-41 P.270<br />Review<br />5-41 <br />μ=100, P(X<115)=0.9<br />(a). σ=11.72<br />(b). Stock at least ___?<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Visualization<br />(X-100)11.72=1.645  <br />z =1.645  <br />X=119.28<br />Therefore, we’dbetter stock at least 120 tubes. <br />
15. 15. The Normal Distribution<br />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? <br />(A) 0.10 (B) 0.18 (C) 0.50 (D) 0.82 (E) 0.90 <br />Group Discussion<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />
16. 16. Self-Practice<br />Chapter 5, No. 5-37 P.270<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Given that a random variable, X, has a normal distribution with mean 6.4 and standard deviation 2.7, find<br />Q1. P (4.0<x<5.0)<br />Q2. P(x>20)<br />Q3. P(x<7.2)<br />Q4. P((x<3.0) or (x>9.0))<br />
17. 17. Chapter 5, No. 5-37 P.270<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Given that a random variable, X, has a normal distribution with mean 6.4 and standard deviation 2.7, find<br />Q1. P (4.0<x<5.0)<br />Q2. P(x>20)<br />Q3. P(x<7.2)<br />Q4. P((x<3.0) or (x>9.0))<br />Self-Practice<br />
18. 18. Sampling and Sampling Distribution<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Population<br />Sample<br />= all items chosen for study<br />= a portion chosen from the population<br />Parameter<br />Statistic<br /> Greek or capital letters<br /> Lowercase Roman letters<br />
19. 19. Standard Error<br />Population Range=80~240<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />µ = 100<br />σ = 25<br />=95<br />Sample Range=90~120<br />=106<br />=101<br />Standard Error of mean<br />Standard Deviation of population<br />____<br />
20. 20. Standard Error<br />Quiz<br />Review<br />Sampling Distribution<br />SPSS<br />Sample size <br />Dispersion of means<br />Standard Error<br />
21. 21. The Normal Distribution<br />SPSS Tip: Descriptive Statistics<br />The data can be downloaded from:<br />Blackboard – Inductive Statsitics STA2—SPSS--Week 2 Creating Graphs.sav<br />
22. 22. SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />Type data into SPSS<br /> - Gender<br /> - Age<br /> - Satisfaction with STA2<br />1 2 3 4 5<br />Hate it -------- Not like it --------- So so------------Like it-----Addicted to it<br />
23. 23. SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />Type data into SPSS<br /> - Gender<br /> - Age<br /> - Satisfactionwith STA2<br />2. Click on “Values” to define variables<br />e.g. 0=male; 1=female<br />1 2 3 4 5<br />Hate it -------- Not like it --------- So so------------Like it-----Addicted to it<br />1. Use the Variable View Tab<br />
24. 24. SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />Type data into SPSS<br /> - Gender<br /> - Age<br /> - Satisfaction with STA2<br />4. Input data intoeach column<br />3. Use the Data View Tab<br />
25. 25. SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />Type data into SPSS<br /> - Gender<br /> - Age<br /> - Satisfaction with STA2<br />5. Don’tforget to choose the measurement level. <br />* . Youcanedit the variables again. <br />
26. 26. 6. Analyze—descriptivestatistics--Descriptive<br />SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />
27. 27. SPSS Tip: Descriptive Statistics<br />Nowyougetit!<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />
28. 28. 7. Analyze—descriptivestatistics--Frequencies<br />SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />
29. 29. 8. Choose the variableyouneed to analyze<br />SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />9. Click “Statistcs” to choose more<br />
30. 30. SPSS Tip: Descriptive Statistics<br />Quiz<br />Sampling<br />Random Sampling<br />Experiment Design<br />Sampling Distribution<br />More about Sampling<br />Nowyougetit!<br />
31. 31. Summary<br />Review of Chapter 5<br />Sampling Distribution<br />SPSS<br />