Introductory Statistics: Unit 1 Study Guide (Statistical Reasoning, Measurement, and Data Visualization)

{"type":"doc","content":[{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Statistical Reasoning and Study Design"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Definitions and Key Concepts"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Statistics (the science):"},{"type":"text","text":" The science of collecting, organizing, and interpreting data."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Statistics (the numbers):"},{"type":"text","text":" Data—numbers or other information that describe or summarize something."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Population:"},{"type":"text","text":" The complete set of people or things being studied."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Population parameter:"},{"type":"text","text":" A number describing a characteristic of the population (usually unknown)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Sample:"},{"type":"text","text":" A subset of the population from which data are actually obtained."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Raw data:"},{"type":"text","text":" The individual measurements or observations collected from the sample."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Sample statistic:"},{"type":"text","text":" A number describing a characteristic of the sample, found by summarizing the raw data."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Rule:"},{"type":"text","text":" Population → parameter; Sample → statistic. Both pairs start with the same letter."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","text":"Example:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"A researcher surveys 800 randomly chosen registered voters in Tennessee and finds that 62% say they have voted in a local election in the past two years."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Population:"},{"type":"text","text":" All registered voters in Tennessee."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Population parameter:"},{"type":"text","text":" The true percentage of all Tennessee registered voters who voted in a local election in the past two years."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Sample:"},{"type":"text","text":" The 800 voters surveyed."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Raw data:"},{"type":"text","text":" Each voter's individual yes-or-no response."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Sample statistic:"},{"type":"text","text":" 62%."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Margin of Error and Confidence Intervals"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Margin of error:"},{"type":"text","text":" The amount by which a sample statistic may vary from the population parameter."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Confidence interval:"},{"type":"text","text":" The range of values likely to contain the population parameter."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Formula:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Lower bound = sample statistic − margin of error"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Upper bound = sample statistic + margin of error"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Written as: sample statistic ± margin of error"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Interpretation:"},{"type":"text","text":" \"The true percentage of [the population] that [does the thing] is between [lower] and [upper].\""}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","text":"Example:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"In a poll of 1,240 adults, 43% said they read a physical newspaper at least weekly. Margin of error is 3 percentage points."}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Lower: 43% − 3% = 40%"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Upper: 43% + 3% = 46%"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Confidence interval: 40% to 46%"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Interpretation: We are confident that the true percentage of all adults who read a physical newspaper at least weekly is between 40% and 46%."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"95% confidence level:"},{"type":"text","text":" If the study were repeated many times, about 95% of the intervals produced would contain the true parameter."}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"The Statistical Study Process"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"State the goal of the study precisely."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Choose a representative sample from the population."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Collect raw data and summarize it by finding sample statistics."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Make inferences about the population from the sample statistics."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Draw conclusions."}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Loop:"},{"type":"text","text":" population → sample → raw data → sample statistics → inference back to population parameters."}]},{"type":"heading","attrs":{"textAlign":null,"level":2},"content":[{"type":"text","text":"Sampling Methods"}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","text":"Definitions"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Census:"},{"type":"text","text":" Collection of data from every member of the population."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Representative sample:"},{"type":"text","text":" One whose relevant characteristics are generally the same as the population's."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Bias:"},{"type":"text","text":" A study suffers from bias if its design or conduct tends to favor certain results."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Random sample:"},{"type":"text","text":" Every member of the population has an equal chance of being selected."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Simple random sample (SRS):"},{"type":"text","text":" Every 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