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Hypothesis Testing with z Tests Chapter 7

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The z Table >Benefits of standardization: allowing fair comparisons >z table: provides percentage of scores between the mean and a given z score

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Raw Scores, z Scores, and Percentages >Step 1: Convert raw score to z score >Step 2: Look up area in Table The table presents area between the Mean and z and beyond the mean and z.

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From Percentages to z Scores >Step 1: Use the z table in reverse, taking a percentage and converting it into a z score. >Step 2: Convert the z score to a raw score using the formula.

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Sketching the Normal Curve >The benefits of sketching the normal curve: Stays clear in memory; minimizes errors Practical reference Condenses the information

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The Standardized z Distribution

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Calculating the Percentile for a Positive z Score

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Calculating the Percentage Above a Positive z Score

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Calculating the Percentage at Least as Extreme as Our z Score

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Calculating the Percentile for a Negative z Score

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Calculating the Percentage Above a Negative z Score

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Calculating the Percentage at Least as Extreme as Our z Score

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Calculating a Score from a Percentile

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Check Your Learning >If the population mean is 10 and the standard deviation is 2: What is the percentile rank of a sample mean of 6? of 11? What percentage of the samples would score higher than a score of 6? of 11?

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The Assumptions and the Steps of Hypothesis Testing >Requirements to conduct analyses Assumption: characteristic about a population that we are sampling necessary for accurate inferences

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Parametric v. Nonparametric Tests >Parametric tests: inferential statistical test based on assumptions about a population >Nonparametric tests: inferential statistical test not based on assumptions about the population

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An Example of the z Test >The z test When we know the population mean and the standard deviation >The z test The six steps of hypothesis testing >H 0, H 1 >One-tailed vs. two-tailed tests

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Determining Critical Values for a z Distribution – One tailed or two- tailed test for significance?

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Making a Decision

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Check Your Learning >IQ scores are designed to have a mean of 100 and a standard deviation of 15. Assume the class mean is 114. Go through the six steps of hypothesis testing.

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“Dirty” Data >“Dirty” Data: Missing data, misleading data, and outliers >Misleading data: The famous butterfly ballot used in Florida during the 2000 presidential election showed the of the arrangement of items on a page.

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Cleaning “Dirty” Data >Judgment calls need to be made. >The best solution is to report everything so that other researchers can assess the trade-offs. >The best way to address the problem of dirty data is replication.

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