Approximately 95 of the data is within 2 standard

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Approximately 95% of the data is within 2 standard deviations of the mean. Approximately 99.7% of the data is within 3 standard deviations of the mean. Standardizing a raw score (finding a z–score) z = x-μ/σ Use the z–score to look up the probability on the table. The probability given in the table is always the area to the left of the z–score. 09.06 Models of Population An experiment is a study that involves separating the sample into two or more groups, applying a treatment to one of the groups, and leaving the other group untreated. Experiments can be used to find cause and effect relationships. An observational study is a study in which control and trial groups are naturally occurring, and observations are made about something of interest to the researcher. Observational studies can be used to find possible relationships. A sample survey is a process for collecting data from a sample by asking questions. A survey cannot be used to show a cause-and-effect relationship. A survey is typically used to describe something about a population that is being studied.
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Simulations can be used to compare theoretical and empirical probabilities and determine how plausible the results are. 09.07 Using Surveys A population proportion is the proportion of a population that has a certain property. The margin of error for the population proportion is given by the formula: Margin of error = z • square root p(1-p)/n z = the z-score that corresponds to the confidence interval p = sample proportion n = sample size The margin of error for the population mean is given by the formula: Margin of error = z • σ/square root n z = the z-score that corresponds to the confidence interval σ = population standard deviation n = sample size
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