AMS 5 Lecture 18: Class 18 - [0][1] Boxes

5 Pages

Applied Math and Statistics
Course Code
Yonatan Katznelson

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AMS 5 Lecture 18 5172017 (8:009:05) [0][1] Boxes In a [0][1]box all the tickets are labeled with a 0 or a 1. o The sum of all the tickets in a [0][1]box is equal to the number of [1]s in the box. o The average of a [0][1]box equals the fraction of [1]s in the box, or equivalently, the percentage of [1]s in the box. o The SD of a [0][1]box is computed using the shortcut: 12 SD box= (p(1p)) o Where p is the fraction of [1]s in box and (1p) is the fraction of [0]s in box. Bernoulli Trial two outcomes Simple Random Samples From a [0][1] Box o A simple random sample of n tickets drawn from a [0][1]box of N tickets is a random sample drawn without replacement. The expected percentage of 1]s in the sample is equal to the percentage of [1]s in the box. If the tickets are drawn with replacement, then the standard error for the percentage of [1]s in the sample is SE SD nbox002 When the tickets are drawn without replacement, then the standard error for the percentage of [1]s in the sample is SE CF * SD nbox 12* 100 where the correction factor is CF = ((Nn)(N1))12 Example: Experiment showed for guesses for 10!, starting from 1 and another group counting from 10. The 10 group overshot, the 1 group undershot. Why should we include the correction factor (CF)? o For simple random samples (random samples without replacement), it is always correct to include the correction factor when calculating the SE. However if the
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