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Lecture 26 - 211 Fall 2009

# Lecture 26 - 211 Fall 2009 - Application Determining crop...

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Unformatted text preview: Application: Determining crop losses. Estimated parameters for cranberry yield distributions: MA Cranberry Yield Means and Standard Deviations: 2002– 2007 (barrels per acre). Year 2002 2003 2004 2005 2006 2007 Mean 199 311 247 169 274 220 St. Dev. 189 74 84 93 113 74 Grower lost 2006 crop due to chem. Contamination. For the period 2002 – 2005, two of the grower’s bogs have, on average, had yields that exceeded the mean: • Bog 1: 9.7 acres; z = 0.43 • Bog 2: 6.5 acres; z = 0.21 W hat are the predicted yields for these bogs in 2006 and 2007? III. Probability, Random Variables and Sampling Distribution. A. Probability (Chapter 5) B. Discrete Random Variables (Chapter 5) C. Continuous Random Variables (Chapter 6) D. Sampling Distribution of the Sample Mean (Chapter 7) Experiment - Handout X = commute distance for residents of a neighborhood. Use Use these data to estimate the population mean. estimate Choose random Choose a random sample of 4 observations. Calculate Calculate the sample mean: sample Choose Choose another random sample of 4 observations. random Add Add to your first sample ⇒ sample of 8 obs. Calculate Calculate the sample mean for n = 8. sample 1 The following represents a population of N = 60. X – commuting distance for one Amherst neighborhood. 13.5 10.4 7.3 12.4 11.4 8.4 10.8 9.4 8.0 12.9 11.5 7.5 13.7 12.4 11.4 9.2 7.5 9.4 8.0 11.4 9.6 12.6 11.0 13.0 5.8 6.5 11.4 12.8 12.6 11.6 10.0 8.4 6.8 8.9 11.7 11.3 10.9 10.4 8.4 9.7 10.1 8.5 6.5 11.7 9.1 10.5 11.4 8.3 8.2 10.7 11.7 7.9 10.8 11.0 7.1 9.3 11.4 10.5 7.2 14.0 D. Sampling Distribution for the Sample Mean 1. Sampling Error (Text - Section 7.1) Estimation – 2. Sampling Distribution for X (Text –Sect. 7.2) Sampling Distribution – distribution for a random variable – Sample mean is a random variable. Why? 2 2. Sampling Distribution Sampling Distribution: characteristics? 2. Sampling Distribution Sampling Distribution – Shape Case 1: Population (X) is normal – Case 2: X is NOT normal – Case 3: Central Limit Theorem (CLT): 2. Sampling Distribution Characteristics – Variation. • When X is normal. • Or, n ≈ 30 or greater (CLT). 3 Experiment Same Same population data. Choose Choose a random sample of 8 observations: observations – Choose another 4 observations – Add them to your sample of n = 4. Calculate Calculate the sample mean for n = 8. x= ∑x n = 8 = Same data – an array! 5.8 8.0 9.2 10.5 11.4 12.4 6.5 8.0 9.3 10.5 11.4 12.4 6.5 8.2 9.4 10.7 11.4 12.6 6.8 8.3 9.4 10.8 11.4 12.6 7.1 8.4 9.6 10.8 11.4 12.8 7.2 8.4 9.7 10.9 11.5 12.9 7.3 8.4 10.0 11.0 11.6 13.0 7.5 8.5 10.1 11.0 11.7 13.5 7.5 8.9 10.4 11.3 11.7 13.7 7.9 9.1 10.4 11.4 11.7 14.0 2. Sampling Distribution Summary Sample Sample mean – another CRV. Sampling Sampling Distribution: – Center: – Standard Error: – Shape: Probabilities Probabilities – 4 ...
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