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Lesson 13-1 Sampling and Bias
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Objectives Identify various sampling techniques Recognize a biased sample
Vocabulary sample – population – census – random sample – simple random sample – stratified random sample – systematic random sample – biased sample – convenience sample – voluntary response sample –
Sampling Techniques Published Data – using data already gathered for a new purpose Survey – asking questions of a group and recording results Observational Study – watching events and recording results Designed Experiment – an study where the designer changes something and results are recorded Census – all members of a population are sampled
Types of Random Samples Simple Random Sample (SRS) – any member is equally likely as any other member to be selected; Basis for all statistical studies Stratified Random Sample – population is divided into similar non-overlapping groups and then a random sample is done on each group; Used to break into groups by known attributes (sex, age, education, income levels, etc) and then SRS Systematic Random Sample – members selected according to specified time or item interval; Used to simulate an SRS by spreading selection out by time or by fixed number of possible selectees
Biased Samples Convenience Samples – members of population that are easily accessed Examples: neighborhood survey, class survey Problems: tends to get participants only from a similar group of people Voluntary Response Samples – only those who want to participate are sampled (a form of convenience) Examples: on-line polls, TV polls, political mailings Problem: tends to get only the very strongly in favor, or opposed, for participants
Example 1a Retail Each day, a department store chain selects one male and one female shopper randomly from each of their 57 stores, and asks them survey questions about their shopping habits. Identify the sample and suggest a population from which it was selected. Answer:The sample is 57 male and 57 female shoppers each day. The population is shoppers in the chain’s stores.
Example 1b Retail Each day, a department store chain selects one male and one female shopper randomly from each of their 57 stores, and asks them survey questions about their shopping habits. Classify the sample as simple, stratified, or systematic. Answer:This is a stratified random sample. The population is divided into similar, nonoverlapping groups.
Example 2a Student Council The student council surveys the students in one classroom to decide the theme for the spring dance. Identify the sample as biased or unbiased. Explain your reasoning. Answer: The sample is biased. The sample includes only students in one classroom.
Example 2b School The Parent Association surveys the parents of every fifth student on the school roster to decide whether to hold a fundraiser. Identify the sample as biased or unbiased. Explain your reasoning. Answer: The sample is unbiased. The parents are picked using a systematic method.
Example 3 Community The chairperson of a neighborhood association has been asked by the association to survey the residents of the neighborhood to find out when to hold a neighborhood clean up day. She decides to ask her immediate neighbors, and the neighbors in the houses directly across the street from her house. A. Identify the sample, and suggest a population from which it was selected. Answer:The sample is the chairperson’s immediate neighbors and the neighbors across the street. The population is the residents of the neighborhood. B. Classify the sample as a convenience sample, or a voluntary response sample. Answer:This is a convenience sample because the chairperson asked only her closest neighbors.
Example 4 School The high school Parent Association sent a letter to the parents of all graduating seniors asking them to return the enclosed ballot if they had a preference on where the graduation party was to be held. A. Identify the sample. Answer:The sample is a group of parents of the graduating seniors. B. Suggest a population from which the sample was selected. Answer:The population is all of the parents of the graduating seniors.
Example 4 cont C. State whether the sample is unbiased (random) or biased. If unbiased, classify it as simple, stratified, or systematic. If biased, classify it as convenience or voluntary response. Answer:The sample is biased. It is a voluntary response sample. The sample includes only the parents of the graduating seniors who return the ballot. Therefore, the reported preference is not likely to be representative of all of the parents.