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Unformatted text preview: 1 Posted after class WEEK 12 – Wed, Nov 17 REVIEW UNIT 2 Chapter 1 Describing Data Sets  Chap 1: Secs 1, 2, 3, 4, 5, 9 Measurement processes applied to subjects or entities produce data. Usually many variables are measured for which data are recorded. You must understand the measurement process and the selection process (and the possible filtering of subjects out of the study after their selection) before you can truly evaluate the importance of the data. Types of variables : Categorical, Numerical Descriptive Statistics for Numerical Data Sets Percentiles, Five Number Summary Mean, Median, Mode Standard Deviation, Range, Interquartile Range Chebyshev Inequality, Empirical Rule Shapes of Distributions, Symmetric, Skewed Tables and Displays StemandLeaf Dotplot Histogram Box Plot Measurement Process Selection Process Subjects Data 2 Example . Consider the following weights (in kg) for a sample of twentytwo guinea pigs. 0.95 0.98 1.14 1.11 1.04 1.03 1.02 1.00 0.95 0.98 0.99 1.06 1.03 1.08 1.01 1.03 1.03 1.18 1.24 0.97 1.00 1.05 Here is a stemandleaf plot of the sample data. 9 557889 10 001233334 10 568 11 14 11 8 12 4 1. The distribution of sample weights is best described as (a) symmetric about its mean (b) skewed toward small values (c) skewed toward large values 2. The sample 75 th percentile is (a) 1.11 kg (b) 1.182 kg (c) 1.025 kg (d) 1.04 kg (e) 1.065 kg Ans. Note that (n + 1)p = 23(.75) = 17.25 and in 17 th position x = 1.06 and in 18 th position x = 1.08. Hence, the 75 th percentile is 1.06 + .25(1.08 – 1.06) = 1.065 3. For this sample , the percentage of guinea pigs with weights greater than the 75 th percentile is (a) 75.0% (b) 22.7% (c) 25.0% (d) 36.4% (e) 27.3% 21 . A sample of 100 weights has Q 1 = 150 lbs, Q 2 = 165 lbs and Q 3 = 190 lbs. The two largest weights in the sample are 243 lbs and 275 lbs. Consider a boxplot of the data. The upper (right) whisker extends to what value? (a) 230 (b) 243 (c) 250 (d) 190 (e) 275 3 Chapter 6 Confidence Interval Estimates  Chap 6: Secs 1, 2, 3, 4, 6 Sample statistics as estimators for population parameters . With simple random sampling (SRS): x is a point estimator of the population mean μ for a numerical characteristic (s is a point estimator of the population standard deviation σ) P ˆ is a point estimator of p for a dichotomous population Facts about the Sampling Distribution of with SRS: Book (N indefinitely large) N specified – Correct Formulas Note: SE stands for what is commonly called Standard Error . It is a samplebased estimate of the Standard Deviation SD . The sample mean has a probability distribution (its sampling distribution) that depends upon the population x i values (generally unknown). If the population x i values are nearly normally distributed, then is nearly normally distributed. In general, when n is large is nearly normally distributed (a result called the Central Limit Theorem ). Therefore, we often take the sampling distribution of to be a normal distribution. to be a normal distribution....
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 Summer '10
 DennisGilliland
 Standard Deviation, Statistical hypothesis testing

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