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Chapter01

# Chapter01 - Chapter 1 Sampling and Descriptive Statistics 1...

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1 Chapter 1. Sampling and Descriptive Statistics

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2 Why Statistics? Uncertainty in repeated scientific measurements Drawing conclusions from data Designing valid experiments and drawing reliable conclusions To be a well informed member of society
3 Example 1 Consider a machine that makes steel rods for use in optimal storage devices. The specification for the diameter of the rods is 0.45 ± 0.02 cm. During the last hour, the machine has made 1000 rods. The quality engineer wants to know approximately how many of these rods meet the specification. He does not have time to measure all 1000 rods. So, he draws a random sample of 50 rods, measures them, and finds that 46 of them (92%) meet the diameter specification. It is unlikely that the sample of 50 rods represents the population of 1000 exactly.

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4 Section 1.1: Sampling Definitions: A population is the entire collection of objects or outcomes about which information is sought. A sample is a subset of a population, containing the objects or outcomes that are actually observed. A simple random sample (SRS) of size n is a sample chosen by a method in which each collection of n population items is equally likely to comprise the sample, just as in the lottery.
5 Example 2 At The State University, there is a professor who is interested in the average height of students at the university. She makes a list of all the 50,000 students at the university and assigns a number to each student. A random number generator generates 100 numbers and the students corresponding to those numbers are selected to have their height measured. This is a simple random sample.

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6 Sampling (cont.) Definition: A sample of convenience is a sample that is not drawn by a well-defined random method. Things to consider with convenience samples: Differ systematically in some way from the population. Only use when it is not feasible to draw a random sample.
7 Example 3 A construction engineer has received a shipment of 1000 concrete blocks, each weighing approximately 50 pounds. The blocks are in a large pile. The engineer wishes to investigate the crushing strength of the blocks by measuring the strengths in a sample of 10 blocks. It may be difficult to take a SRS since that would involve getting blocks from the middle and bottom of the pile, so the engineer may just take 10 off the top. This would a sample of convenience.

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8 Sampling Variation A SRS is not guaranteed to reflect the population perfectly. SRS’s always differ in some ways from each other; occasionally a sample is substantially different from the population. Two different samples from the same population will vary from each other as well. This phenomenon is known as sampling variation .
9 Example 1 cont. Remember the rod example?

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