This preview shows pages 1–14. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Sampling Distributions and Estimation k MGMT 670: Business Analytics Krannert School of Management Purdue University 2 § Involves • Estimation • Hypothesis testing § Purpose • Estimate and draw conclusions about population parameters. • Proper sampling methods provides “good” estimates. Statistical Inference Population? 3 Process of Statistical Inference 1. Population consists of all elements of interest. 2. Collect a sample . 3. The sample data provide a summary of the sample or sample statistic . 4. The value of the sample statistic is used to make an estimate of the population parameter . 4 Examples § The owner of the Boilers’ House, a recently opened gourmet restaurant, hopes to estimate the average demand for hot dog after a home football game. Using the data from the last two years, his estimate is 452. § A manufacturer claims that the defective rate of his process is at most 2%. To find out whether the statement is true, we randomly drew a sample of 30 items and found 5 defective items. 5 Sampling Methods Simple Random Sampling Stratified Random Sampling Cluster Sampling Systematic Sampling Probability Sampling Non Probability Sampling Convenience Sampling Judgment Sampling 6 Simple Random Sampling § Finite Population of Size N • Each possible sample of size n has the same probability of being selected. • Sampling with replacement • Sampling without replacement • Random numbers are often used (many software packages have this capability). § Infinite Population • Each element is selected independently. 7 Use Minitab to Generate Random Samples 8 Enter the sample size and new variable name 9 Rolling a die … Each face of die and its frequency 500 1000 1500 2000 2500 3000 3500 4000 4500 1 2 3 4 5 6 Possible values are: 1, 2, 3, 4, 5, 6. 3.5 1.70783 μ σ = = 10 How does the average of 5 rolls behave? roll Face 1st 3 2nd 2 3rd 3 4th 5 5th 2 Average 3 carried out the experiment 5000 times count of averages of 5 rolls 100 200 300 400 500 600 1 1 . 4 1 . 8 2 . 2 2 . 6 3 3 . 4 3 . 8 4 . 2 4 . 6 5 5 . 4 5 . 8 =3.5 =0.7637 11 How does average of 40 rolls behave? count of average of 40 rolls 50 100 150 200 250 300 350 400 2 . 4 9 2 . 6 4 2 . 7 9 2 . 9 4 3 . 9 3 . 2 4 3 . 3 9 3 . 5 4 3 . 6 9 3 . 8 4 3 . 9 9 4 . 1 4 4 . 2 9 4 . 4 4 4 . 5 9 =3.5 =0.27 12 § Sampling Distribution of : • Mean of • Standard Deviation of Each face of die and its frequency 500 1000 1500 2000 2500 3000 3500 4000 4500 1 2 3 4 5 6 count of averages of 5 rolls 100 200 300 400 500 600 1 1 . 4 1 . 8 2 . 2 2 . 6 3 3 . 4 3 . 8 4 . 2 4 . 6 5 5 . 4 5 . 8 n=1 50 100 150 200 250 300 350 400 1 1 . 4 4 1 . 8 9 2 . 3 4 2 . 7 9 3 . 2 4 3 . 6 9 4 . 1 4 4 . 5 9 5 . 4 5 . 4 9 5 . 9 4 X Comparison n=5 n=40 X X =0.2700 =0.7637 =1.7078 13 Standard Deviation of Sample Mean § Measures variability in sample mean § Referred to as the standard error of the mean § Less than population standard deviation § Formula n x σ σ = 1 = N n N n x σ...
View
Full
Document
This note was uploaded on 10/17/2011 for the course MGMT 670 taught by Professor Tawarmalani during the Spring '11 term at Purdue University.
 Spring '11
 Tawarmalani
 Management

Click to edit the document details