Inductive StatisticsInductive Statistics
Dr. Ning DING
I.007 IBS, Hanze
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Review:Chapter 5 Probability DistributionChapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known* when σ is unknown* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known* when σ is unknown AND n=<30
~Test for Proportion
Table of Contents
Chapter 5: Probability Distribution
BionomialDistributionBionomial
DistributionPoisson
DistributionPoisson
Distribution
Discretewithin a range
Normal Distribution
Normal Distribution
continuousDiscretewith mean
λ: meanp: probability of success
q: probability of failure
q = 1- p
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
60 80
The student is doing better in Chemistry than in biology. Is it correct?
Test Score Class mean SD z score
Biology 60 50 5 +2
Chemistry 80 90 10 -1
The student is actually doing better in biology.
Chapter 5: Probability DistributionChemistry
standardized scalestandardized scale
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Chapter 6: Sampling Distribution
Sample size Sample size
Dispersion of sample meansDispersion of sample means
Standard ErrorStandard Error
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Infinitepopulation
Infinitepopulation
Finite population
Finite population
Chapter 6: Sampling DistributionReview:
-Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
confidence levelconfidence level
confidence intervalconfidence interval
Chapter 7: Estimation
Upper tailLower tail
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates & Confidence Intervals
= the probability that we associate with an interval estimate
It is the range of the estimate we are making.
-1.64σ-1.64σ +1.64σ+1.64σ
90%90%90% confident that our population mean will lie within this interval.
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Chapter 7 Estimation
Interval Estimates of the Mean
Interval Estimates of the Proportion
σ is known:σ is known:
σ is unknown:σ is unknown:
n <30 & σ is unknownn <30 & σ is unknown
•Degree of freedom •Confidence Level
Interval Estimates of the mean from Large SamplesEstimate the mean life of windshield wiper. The standard deviation of the population life is 6 months. We randomly select 100 wiper blades and know the mean is 21 months.
Example:Example:
Step 1: List the known variablesStep 1: List the known variables
Step 2: Calculate the standard error of the meanStep 2: Calculate the standard error of the mean
n=100 σ=6 months
Ch 7 Example P.361
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the mean from Large SamplesEstimate the mean life of windshield wiper. The standard deviation of the population life is 6 months. We randomly select 100 wiper blades and know the mean is 21 months.
Example:Example:
Step 3: If we choose 95% confidence level, find the z scoreStep 3: If we choose 95% confidence level, find the z score
-1.96σ-1.96σ
95%95%
+1.96σ+1.96σ
Appendix Table 1Appendix Table 1
47.5%47.5% 47.5%47.5%
Ch 7 Example P.361
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the mean from Large SamplesEstimate the mean life of windshield wiper. The standard deviation of the population life is 6 months. We randomly select 100 wiper blades and know the mean is 21 months.
Example:Example:
Step 4: Calculate the upper and lower limitsStep 4: Calculate the upper and lower limits
19.8219.82 22.1822.18
95%95%
Ch 7 Example P.361
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the mean from Large Samples
Suppose we don’t know the population standard deviation
Example:Example:
Find the interval estimate of the mean annual income of 700 families at 90% confidence level.
Step 1: Estimate the population standard deviation.Step 1: Estimate the population standard deviation.
Step 2: Find the standard error of the mean Estimate the mean. Step 2: Find the standard error of the mean Estimate the mean.
Ch 7 Example P.363
n/N = 50/700 = 0.0714 >.05 Use F.P.M.
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the mean from Large Samples
Suppose we don’t know the population standard deviation
Example:Example:
Find the interval estimate of the mean annual income of 700 families at 90% confidence level.
Step 2: Find the standard error of the mean Estimate the mean. Step 2: Find the standard error of the mean Estimate the mean.
Ch 7 Example P.363
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the mean from Large Samples
Step 3: Find the z scoreStep 3: Find the z score
-1.64σ-1.64σ +1.64σ+1.64σ
Appendix Table 1Appendix Table 1
Example:Example:Find the interval estimate of the mean annual income of 700 families at 90% confidence level.
90%90%
45%45% 45%45%
Ch 7 Example P.363
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the mean from Large Samples
11,587.5011,587.50 12,012.5012,012.50
Example:Example:Find the interval estimate of the mean annual income of 700 families at 90% confidence level.
Step 4: Calculate the upper and lower limitsStep 4: Calculate the upper and lower limits
90%90%
45%45% 45%45%
Ch 7 Example P.363
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates Using t Distribution
• Sample size < 30
• Unknown population standard deviation
• Sample size < 30
• Unknown population standard deviation
1. Degree of Freedom1. Degree of Freedom
b=6
b=13
... ...
degree of freedomdegree of freedom
n-1n-1n-1n-1
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates Using t Distribution2. Using the 2. Using the tt Distribution Table Distribution Table Appendix Table 2Appendix Table 2Appendix Table 2Appendix Table 2
Confidence IntervalConfidence Intervaldegree
of
freedom
degree
of
freedom
77
0.050.05
2.365
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates Using t Distribution
Example:Example:The plant manager wants to estimate the coal needed for this year. He took a sample by measuring coal usage for 10 weeks.
Step 1: Calculate the standard error of the mean Step 1: Calculate the standard error of the mean
9
Step 2: Look in Appendix Table 2 to get the t valueStep 2: Look in Appendix Table 2 to get the t value t = 2.262
95%
Step 3: Calculate the upper and lower limitsStep 3: Calculate the upper and lower limits
The manager is 95% confident that the mean weekly usage of coal lies between 10,899 and 11,901 tons.
Ch 7 Example P.373
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the proportion from Large Samples
Mean of the Sampling Distribution of the Proportion
Standard Error of the Proportion
Esitmated Standard Error of the Proportion
unemployment rate is a proportion
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the proportion from Large Samples
Example:Example:What proportion of employees prefer to provide their own retirement benefits in lieu of a company-sponsored plan?
n = 75 n = 75 Step 1: Conduct simple random samplingStep 1: Conduct simple random sampling
Step 2: QuestionnaireStep 2: Questionnaire Agree or Disagree
30 vs. 45
Step 3: Calculate the estimated error of the proportion
Step 3: Calculate the estimated error of the proportion
Ch 7 Example P.368
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Interval Estimates of the proportion from Large Samples
Example:Example:What proportion of employees prefer to provide their own retirement benefits in lieu of a company-sponsored plan?
Step 4: Use the confidence level to find z scoreStep 4: Use the confidence level to find z score 99%99%
-2.58σ-2.58σ
99%99%
49.5%49.5% 49.5%49.5%
+2.58σ+2.58σ
Step 5: Estabilish of the upper and lower limitsStep 5: Estabilish of the upper and lower limits
0.2530.253 0.5470.547 99% sure that 25.3% to 54.7% of the employees agreed with this plan
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknown AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:BasicsVocabularyVocabulary
•hypothesis hypotheses
•Likelihood
•Significant
•Accept / Reject
hypothese Hypothese hipótesis гипотеза 假设 l'hypothèse
la probabilité 可能性 вероятность Wahrscheinlichkeit waarschijnlijkheid probabilidad
significativo signifikant significant significative значительный 显著
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:Basics
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 ≠ 10
For example:
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:Practice
Ch 8 No. 8-24 P.415
The STA department installed energy-efficient lights, heaters and air conditioners last year. Now they want to determine whether the average monthly energy usage has decreased. Should they perform a one- or two-tailed test?
If their previous average monthly energy usage was 3,124 kw hours, what are the null and alternative hypotheses?
Answer: One-tailed test lower-tailed test
8-248-24Review:
-Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:two-tailed test
Ch 8 Example P.417
Assume that a manufacturer supplies axles which must withstand 80,000 pounds per square inch. Experiences show the standard deviation is 4,000 pounds. Being either lower or greater is not allowed. He sampled 100 axles from the production and found the mean is 79,600 pounds. Example:Example:
Step 1: List the known variablesStep 1: List the known variables
Step 2: Formulate the hypothesesStep 2: Formulate the hypotheses
Step 3: Calculate the standard error
Step 3: Calculate the standard error
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:two-tailed test
Ch 8 Example P.417
Assume that a manufacturer supplies axles which must withstand 80,000 pounds per square inch. Experiences show the standard deviation is 4,000 pounds. Being either lower or greater is not allowed. He sampled 100 axles from the production and found the mean is 79,600 pounds. Example:Example:
Step 4: Visualize the confidence levelStep 4: Visualize the confidence level
-1.96 +1.96
Step 5: Establish the limitsStep 5: Establish the limits
79,216 80,784
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:one-tailed test
Ch 8 Example P.419
Hospital uses large quantities of packaged doses of a drug. The individual dose is 100 cc. The body can pass off the excessive but insufficient doses will be problematic. The hospital knows the standard deviation of the supplier is 2 cc. They sampled 50 doses randomly and found the mean is 99.75 cc. Example:Example:
Step 1: List the known variablesStep 1: List the known variables Step 2: Formulate HypothesesStep 2: Formulate Hypotheses
Step 3: Calculate the standard errorStep 3: Calculate the standard error
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:one-tailed test
Ch 8 Example P.419
Hospital uses large quantities of packaged doses of a drug. The individual dose is 100 cc. The body can pass off the excessive but insufficient doses will be problematic. The hospital knows the standard deviation of the supplier is 2 cc. They sampled 50 doses randomly and found the mean is 99.75 cc. Example:Example:
Step 4: Visualize the confidence levelStep 4: Visualize the confidence level
Step 5: Calcuate the z valueStep 5: Calcuate the z value
-1.28
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses: Practice
Ch 8 No. 8-26 P.422
8-268-26 Step 1: List the known variablesStep 1: List the known variables
Step 2: Formulate HypothesesStep 2: Formulate Hypotheses
Step 3: Calculate the standard errorStep 3: Calculate the standard error
Step 4: Visualize the confidence levelStep 4: Visualize the confidence level
Step 5: Calcuate the z valueStep 5: Calcuate the z value
P=0.48 z=-2.05
-2.05
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses: Practice
Ch 8 No. 8-26 P.422
8-278-27 Step 1: List the known variablesStep 1: List the known variables
Step 2: Formulate HypothesesStep 2: Formulate Hypotheses
Step 3: Calculate the standard errorStep 3: Calculate the standard error
Step 4: Visualize the confidence levelStep 4: Visualize the confidence level
Step 5: Calcuate the z valueStep 5: Calcuate the z value
P=0.475 z= 1.96
-1.96 +1.96
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Ch 8 No. Example P.433
Example:Example:
Step 1: List the known variablesStep 1: List the known variables
Step 2: Formulate HypothesesStep 2: Formulate Hypotheses
Step 3: Calculate the standard errorStep 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 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Ch 8 No. Example P.433
Example:Example:
Step 4: Visualize the confidence levelStep 4: Visualize the confidence level Step 5: Calcuate the t valueStep 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 2Appendix Table 2
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Ch 8 No. Example P.433
Step 4: Visualize the confidence levelStep 4: Visualize the confidence level
Appendix Table 2Appendix Table 2
Confidence IntervalConfidence Intervaldegree
of
freedom
degree
of
freedom
1212
0.05 0.10 0.05 0.10
1.782
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
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 AND µ < 2
For example:
Mea
nM
ean
Proporti
on
Proporti
on
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
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:Example:Step 1: List the known variablesStep 1: List the known variables
Step 2: Formulate HypothesesStep 2: Formulate Hypotheses
Step 3: Calculate the standard errorStep 3: Calculate the standard errorPro
portion
Proporti
on
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
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:Example:Step 4: Visualize the confidence levelStep 4: Visualize the confidence level
Step 5: Calculate the z scoreStep 5: Calculate the z score
Proporti
on
Proporti
on
Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Chapter 8 Testing Hypotheses:Practice
Ch 8 SC 8-9 P.431
.
Step 4: Visualize the confidence levelStep 4: Visualize the confidence level
Step 5: Calculate the z scoreStep 5: Calculate the z score
Proporti
on
Proporti
onStep 1: List the known variablesStep 1: List the known variables
Step 2: Formulate HypothesesStep 2: Formulate Hypotheses
Step 3: Calculate the standard errorStep 3: Calculate the standard error
SC 8-9SC 8-9Review:-
Chapter 5 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
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 Probability Distribution
-Chapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known
* when σ is unknown
* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known
* when σ is unknwn AND n=<30~Test for Proportion
Summary
Review:Chapter 5 Probability DistributionChapter 6 Sampling Distribution
Chapter 7 Estimation~Interval Estimation for Mean
* when σ is known* when σ is unknown* when σ is unknown AND n=<30
~Interval Estimation for Proportion
Chapter 8 Testing Hypothesis~Basics~Two- and One-tailed Test~Test for Mean
* when σ is known* when σ is unknwn AND n=<30
~Test for Proportion
Connection with BRM(Business Research Methods)
Connection with BRM(Business Research Methods)
P.354
The Normal DistributionSPSS 1st Assessment
The data can be downloaded from:
Blackboard – Inductive Statsitics STA2—SPSS--Week 3 Creating Graphs.sav
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