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Chapter 8

# Chapter 8 - KVANLI PAVUR KEELING Chapter8 Statistical...

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Click to edit Master subtitle style   Chapter 8 Statistical  Inference and  Sampling KVANLI PAVUR KEELING

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3/10/11 Chapter Objectives At the completion of this chapter, you should be able to: ∙ Define and distinguish between sample statistics and population parameters ∙ Discuss the Central Limit Theorem and
3/10/11 What’s New in This Chapter? Usually population means (μ) are unknown and have to be estimated To estimate μ, get a sample and find the sample mean, X X estimates μ This is a parameter since it describes the population This is a statistic since it is derived from a sample

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3/10/11 Estimating the Population Mean This chapter discusses how good (reliable) this estimate is The first two sections in this chapter pretend that the population mean (μ) is known We do this to get some idea how the sample mean, X, “behaves”
3/10/11 How Does the Sample Mean Behave? Suppose we were to get sample after sample, finding the sample mean each time If we put these sample means into Excel and told it to make a histogram, what would it look like In particular, does the histogram have a bell-shaped (normal) appearance?

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3/10/11 Example 8.2 Remember : For the first two sections, we’re pretending we know the population mean, μ In this example, we’re interested in X = lifetime of a high-intensity light bulb This example contains 20 samples of n = 10 bulbs each
3/10/11 The Population Shape for X = Lifetime of Bulb μ = X 450 500 550 350 300 250 Bulb lifetimes (in hours) are in here σ is 50 hours

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3/10/11 20 Samples: X = Lifetime of Bulb Columns Q, R, S, T contain the last four samples Column V contains the 20 sample means followed by a summary of these means Column W contains the 20 sample standard deviations Notice 1) The sample means are hanging around 400 2) The sample standard deviations are hanging around 50
3/10/11 The Main Thing The sample means don’t jump around as much (they have less variation) as the individual values Look at the variation in any of the samples in columns Q, R, S, and T Observe how much more variation there is in these four samples as compared to the This is much less than 50

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3/10/11 X = Male Height X = Ht. . 25 6’ 6.25’ 6.5’ 5.5’ . 25 5.25’ 5’ Nearly all heights are in here This is picture #1: the shape of the population
3/10/11 Looking at the Sample Means: Picture #2 5.75’ X 5.775’ 5.8’ 5.825 5.725’ 5.7’ 5.675 Nearly all sample means are in here This is the curve describing the average of n = 100 heights (measureme nts) ' 025 . 10 ' 25 . 100 ' 25 . = = This is a skinny normal curve

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3/10/11 A Whole Lot of Heights The spreadsheet shown on the next two slides contains 50 samples of male heights Each sample contains 100 heights These are not actual heights but were computer generated Each sample was selected from a normal population with a mean of
3/10/11 The First 5 Samples of Heights The first 12 rows The last 5 rows

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3/10/11 The Last 5 Samples of Heights The first 12 rows The last 5 rows
3/10/11 First Question What proportion of male heights is > 5.8’?

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Chapter 8 - KVANLI PAVUR KEELING Chapter8 Statistical...

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