M670_6(Estimation)

# M670_6(Estimation) - 1 Sampling Distributions and...

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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...
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## 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.

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M670_6(Estimation) - 1 Sampling Distributions and...

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