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Lecture 13: Review One-Sample z-test and One-Sample t-test 2011, 11, 1

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Statistical Test 1. How to tell if it is a one-sample z-test or one- sample t-test? 2. What are t-distributions? 3. How to conduct a one-sample t-test? 4. When to reject the null hypothesis?

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One-Sample z-Test When the population mean ( ) and Std. Dev. ( ) are KNOWN, we use one-sample z-test to compare a single sample mean to the known population mean ( ). Key: Look for Population Std. Dev. ( )

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One-Sample t-Test When the population Std. Dev. ( ) is UNKNOWN, we use one-sample t-test to compare a single sample mean to the known population mean ( ). We use the sample standard deviation (S) to estimate the Std. Err. Key: Look for Population Std. Dev. ( )

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Population: By guessing = 10 = ? = sample mean n = 9 Probability Mean Distribution of Sample Means:

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Distribution of Sample Means: t – Distributions n > 100, Normal Distribution n = 9; df = 9 – 1 = 8 n = 70, df = 70-1 = 69

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Determine 1-Tailed or 2-Tailed Test Key 1: Look at the alternative hypothesis (H 1 : > 10) Key 2: Draw the distribution

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Critical Region for One-Tailed Test p <.01 p <.05 =.05 =.01 Critical region

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Determine 1-Tailed or 2-Tailed Test Key 1: Look at the alternative hypothesis (H 1 : 3) Key 2: Draw the distribution

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Critical Regions for Two-Tailed Test p =.005 p =.025 p =.005 =.01 =.05

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Recap today ’ s lecture 1. How to tell if it is a one-sample z-test or one-sample t-test? 2. What are t-distributions? 3. How to conduct a one-sample t-test? 4. When to reject the null hypothesis?

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