Lesson 05 chapter 8 hypothesis testing
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Inductive Statistics Dr. Ning DING [email protected] I.007 IBS, Hanze You’d better use the full-screen mode to view this PPT file.
Transcript of Lesson 05 chapter 8 hypothesis testing
Inductive StatisticsDr. Ning [email protected]
I.007 IBS, Hanze
You’d better use the full-screen mode to view this PPT file.
Table of Contents
Review:Chapter 5 Probability DistributionChapter 6 Sampling DistributionChapter 7 Estimation
Chapter 8 Testing Hypothesis~Test for Mean
* when σ is known* when σ is unknown AND n=<30
~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests~Basics~Independent Sample Test
~Large Samples~Small Samples
~Dependent Sample Test
Chapter 5: Probability DistributionNormal
Distribution continuous
z=1.00 P=0.3413
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 5: Probability DistributionNormal
Distribution continuous
z=±1.00 P=0.6826
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 6 Sampling DistributionInfinite
population Finite
population
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 7 Estimation
Interval Estimates of the Mean
Interval Estimates of the Proportion
σ is known:
σ is unknown:
n <30 & σ is unknown •Degree of freedom •Confidence Level
Chapter 8 Testing Hypotheses-Summary
Ch 8 Example P.417
H0 H1There is no difference between the sample mean and the hypothesized population mean.
There is a difference between the sample mean and the hypothesized population mean.
Two-tailedtest
One-tailedtest
H0 : µ = 10
H1 : µ > 15
H1 : µ < 2
H1 : µ ≠ 15
For example:
Mean
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 8 Testing Hypotheses: Practice8-28 Step 1: List the known variables
Step 2: Formulate Hypotheses
Step 3: Calculate the standard errorStep 5: Calculate the z value
σ=18.4 n=20 954
0.05P=0.45
z=-1.645
Step 4: Visualize the confidence level
With acceptance region accept H0
so, new bulb producing is good!
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Ch 8 No. Example P.433
Example:
Step 1: List the known variables
Step 2: Formulate Hypotheses
Step 3: Calculate the standard error
The HR director thinks that the average aptitude test is 90. The manager sampled 20 tests and found the mean score is 80 with standard deviation 11.
If he wants to test the hypothesis at the 0.10 level of significance, what is the procedure?
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Ch 8 No. Example P.433
Example:
Step 4: Visualize the confidence level Step 5: Calcuate the t value
The HR director thinks that the average aptitude test is 90. The manager sampled 20 tests and found the mean score is 80 with standard deviation 11.
If he wants to test the hypothesis at the 0.10 level of significance, what is the procedure?
Appendix Table 2
t=-1.729 +1.729
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Ch 8 No. Example P.433
Step 4: Visualize the confidence level
Appendix Table 2
Confidence Intervaldf
12
0.05 0.10
1.782
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 8 Testing Hypotheses-Summary
Ch 8 Example P.417
H0 H1There is no difference between the sample mean and the hypothesized population mean.
There is a difference between the sample mean and the hypothesized population mean.
Two-tailedtest
One-tailedtest
H0 : µ = 10
H1 : µ > 15
H1 : µ < 2
H1 : µ ≠ 15
For example:
Mean
Proportion
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 8 Testing Hypotheses:Proportion
Ch 8 Example P.427
HR director tell the CEO that the promotability of the employees is 80%. The president sampled 150 employees and found that 70% are promotable.
The CEO wants to test at the 0.05 significance level the hypothesis that 0.8 of the employees are promotable.
Example:Step 1: List the known variables
Step 2: Formulate Hypotheses
Step 3: Calculate the standard error Proportion
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 8 Testing Hypotheses:Proportion
Ch 8 Example P.427
HR director tell the CEO that the promotability of the employees is 80%. The president sampled 150 employees and found that 70% are promotable.
The CEO wants to test at the 0.05 significance level the hypothesis that 0.8 of the employees are promotable.
Example:Step 4: Visualize the confidence level
Step 5: Calculate the z score
Proportion
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 8 Testing Hypotheses:Practice
Ch 8 SC 8-9 P.431
.
Step 4: Visualize the confidence level
Step 5: Calculate the z score
Step 1: List the known variables
Step 2: Formulate Hypotheses
Step 3: Calculate the standard error
SC 8-9
ProportionReview:
Chapter 5 Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 8 Testing Hypotheses: Measuring Power of a Hypothesis Test
True Not True
Accept
Reject
H0
Type I Error
Type II Error
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Test Hypotheses for the Mean
Test Hypotheses for the Proportion
σ is known
σ is unknown
n <30 & σ is unknown
Chapter 8 Testing Hypotheses--Summary
large sample
small sample
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 8 Testing Hypotheses--Summary
H0: µ=XX
Two-tailedtest
One-tailedtest
H1 : µ > XX
H1 : µ < XX
H1 : µ ≠ XX
Get critical z or t value
α=0.05 z: P=0.45 z= +1.645t: α=0.10
α=0.05 z: P=0.475 z= ±1.96t: α=0.10
α=0.05 z: P=0.45 z= -1.645t: α=0.10
Chapter 9 Testing Hypotheses: Two-Sample Tests
Let’s compare !
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
80
Chapter 9 Testing Hypotheses: Two-Sample Tests: Basics
Independent Samples Dependent Samples
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Basics-Independent
σ is known:
σ is unknown:
H0H1
Two-tailedtest
One-tailedtest
n <30 & σ is unknown
Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples9.1.1 Difference between means: Large Samples
Example:
Ch 9 Example P.456
Whether the hourly wages of semiskilled workers are the same between females and males. The survey showed:
Gender Mean hourly wages from
sample
Standard Deviation of
Sample
Sample size
Female $8.95 $.40 200Male $9.10 $.60 175
Step 1: Formulate hypotheses Two-tailed Test
Step 2: Find the Estimated Standard Error of Difference
Estimated Standard Error of Difference
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests : Two-Independent Samples
z=-1.96 +1.96
Step 3: Visualize and find the z values
Step 2: Find the Standard Error
Ch 9 Example P.456
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples9.1.1 Difference between means: Large Samples
Example:
Ch 9 Example P.456
Whether the hourly wages of female semiskilled workers are lower than that of males. The survey showed:
Gender Mean hourly wages from
sample
Standard Deviation of Sample
Sample size
Female $8.95 $.40 200
Male $9.10 $.60 175
Step 1: Formulate hypotheses One-tailed Test
P=0.45
z=-1.645
Step 2: Visualize and find the z values
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice
Ch 9 No.9-2 P.460
Step 1: Formulate hypotheses9-2P=0.48 z=
Step 2: Find the Standard Error
Step 3: Visualize and Calculate the z scores
- 2.05
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples
9.1.2 Difference between means: Small Samples
Example:
Ch 9 Example P.462
Which program is more effective in raising sensitivity? The survey showed:Program Mean
Sensitivity from sample
Estimated Standard Deviation of Sample
Sample size
Formal 92 15 12
Informal 84 19 15
Step 1: Formulate hypotheses
One-tailed Test
Step 2: Find the Pooled Estimate of σ2
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples
9.1.2 Difference between means: Small Samples
Ch 9 Example P.462
Program Mean Sensitivity
from sample
Estimated Standard Deviation of Sample
Sample size
Formal 92 15 12
Informal 84 19 15
t=1.708
Step 3: Calculate the standard error
Step 4: Visualize and find the t scores
df=(12-1)+(15-1)=25Areas in both tails combined=0.10
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice
Ch 9 No. 9-9 P.466
Step 1: Formulate hypotheses
9-9
Step 2: Find the Pooled Estimate of σ2
Step 3: Calculate the standard error
Step 4: Visualize and Find the t scores
Gender Mean Standard Deviation
Sample size
Female 12.8 1.0667 10Male 11.625 1.4107 8
One-tailed Test
df = 16 area=0.10 t=1.746
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples9.2 Dependent Samples
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples9.2 Dependent Samples
Ch 9 Example P.468
Will the participant lose more than 17 pounds after the weight-reducing program? The survey data is:
Step 1: Formulate Hypotheses
One-tailed Test
Example:Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples9.2 Dependent Samples
Ch 9 Example P.468
Step 2: Calculate the estimated standard deviation of the population difference
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples9.2 Dependent Samples
Ch 9 Example P.468
Step 3: Find the Standard Error of the population difference
Step 4: Calculate the t value
Step 5: Visualize and get the t values
df = 10-1=9 area = 0.10
t=1.833
One-tailed Test
reject H0
significant difference
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice
Ch 9 No. 9-15 P.474
Step 4: Visalize and Calculate the t values
t=-1.895
9-15
Step 3: Find the Standard Error of the population difference
Step 1: Formulate Hypotheses
Step 2: Calculate the estimated standard deviation of the population difference
One-tailed Test
df=7 area=0.10 reject H0
sig difference
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Summary
Review:Chapter 5 Probability DistributionChapter 6 Sampling DistributionChapter 7 Estimation
Chapter 8 Testing Hypothesis~Test for Mean
* when σ is known* when σ is unknown AND n=<30
~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests~Basics~Independent Sample Test
~Large Samples~Small Samples
~Dependent Sample Test
Connection with BRM(Business Research Methods)
Connection with BRM(Business Research Methods)
P.354
The Normal DistributionSPSS Tips
The data can be downloaded from:
Blackboard – Inductive Statsitics STA2—SPSS--Week 5 Correlation and Regression.sav
The Normal DistributionSPSS TipsOur research data is as below:
in our research, we are interested in the relationship between the mean response time and the total number correct for 30 puzzles. We obtained scores on 25 adults who are between the ages of 70 and 80 and are not cognitively impaired.
Please run the SPSS analysis to explore the relationship between the two variables, Latency and Accuracy.
Variable DescriptionLatency Mean response time for 30 puzzlesAccuracy Total number correct for 30 puzzles
The Normal DistributionSPSS Tips
Step 1: Click Analyze Correlate Bivariate
The Normal DistributionSPSS Tips
Step 2: Double click on the variables to move to the Variables box
The Normal DistributionSPSS Tips
Step 3: Check it is a two- or one-tailed test and click Options
The Normal DistributionSPSS Tips
Step 4: Click Means and Standard Deviations
The Normal DistributionSPSS Tips
The Normal DistributionSPSS Tips Step 5: Click GraphLegacy Dialogs Scatter/Dot...
The Normal DistributionSPSS Tips
Step 6: Choose Scatter/Dot Simple scatterplot
The Normal DistributionSPSS TipsStep 7: Choose variables for X,Y axis respectively.
The Normal DistributionSPSS TipsNow you know something about the correlation, but how can you get the regression line as below?
The Normal DistributionSPSS Tips
The correlation between latency and accuracy is -.545, indicating the greater the latency the less the accuracy. The p value of .005 indicates we reject at the .05 level the null hypothesis that latency and accuracy are linearly unrelated in the population.
An examination of the bivariate scatterplot supports the conclusion that there is a fairly strong negative linear relationship between the two variables.
Interpretation:
