Lesson 02 class practices

transcript

Statistics 2Statistics 2

Dr. Ning DING

IBS I.007

n.ding@pl.hanze.nl

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

Review

Sampling Distribution

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

Review

BionomialDistribution

Poisson Distribution

Discretewithin a range

Normal Distribution

continuousDiscretewith mean

Probability of r successes in n trials =

r ! (n-r) !

pr qn-rλ: mean

A-3 A-13 A-1

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

Review

2. From Binomial Distribution to Normal Approximation

Normal approximation

N=50 p=0.25

(a). P(x>10)=?

Review

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)

Review

Normal Distribution

continuous

Step 3: Find CCF (Continuity Correction Factor)

Discrete:

Continuous:

1 2 3 4 5 6 7 8

CCF X>3.5

CCF X>2.5

CCF X<2.5

CCF X<3.5

Review

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

Review

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

Review

3. If P is known, but cannot be found in the table, it is allowed to use the closest one.

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

Review

μ=100, P(X<115)=0.9(a). σ=?

Visualization

z =1.28

z =1.28=(115-100)/σσ=11.72

Review

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.

Review

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

Review

Self-Practice

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))

Review

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

Review

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

Review

Standard Error

µ = 100σ = 25

Population Range=80~240

Sample Range=90~120

Standard Error of mean

Standard Deviation of population____

Review

Standard Error

Sample size

Dispersion of means

Standard Error

Review

The Normal DistributionSPSS Tip: Descriptive Statistics

The data can be downloaded from:

Blackboard – Inductive Statsitics STA2—SPSS--Week 2 Creating Graphs.sav

Sampling

Random Sampling

Experiment Design

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

Sampling

Random Sampling

Experiment Design

More about Sampling

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

Sampling

Random Sampling

Experiment Design

More about Sampling

4. Input data into each column

3. Use the Data View Tab

Sampling

Random Sampling

Experiment Design

More about Sampling

5. Don’t forget to choose the measurement level.

* . You can edit the variables again.

Sampling

Random Sampling

Experiment Design

More about Sampling

SPSS Tip: Descriptive Statistics6. Analyze—descriptive statistics--Descriptive

Sampling

Random Sampling

Experiment Design

More about Sampling

Now you get it!

Sampling

Random Sampling

Experiment Design

More about Sampling

7. Analyze—descriptive statistics--Frequencies

Sampling

Random Sampling

Experiment Design

More about Sampling

8. Choose the variable you need to analyze

9. Click “Statistcs” to choose more

Sampling

Random Sampling

Experiment Design

More about Sampling

Now you get it!

Summary

1. Review of Chapter 5

2. Sampling Distribution

3. SPSS

Lesson 02 class practices

Education