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Unformatted text preview: Tests concerning a population mean. Â¡ Â¢ Â£ Â¤ Â£ Â¡ The mean of a random sample from a population provides a foundation for creating a test statistic to assesses hypothesis about a population mean . Case 1. The population is from the normal family with mean Â¥Â¦ The standard deviation Â§ is known. Â¨ Â¤ Â© Âª Â«Â¬Â Â§ Â®Â¯ Â° has a standard normal distribution . Â± Â¤ Â²Â³Â´Â«Â Âµ Â¶ Â² Â· Â°Â®Â¸Â¶ is the test statistic. Case 2. The population is from an unknown family with mean Â¥Â¦Â¬ The random sample is large (n > 40 rule of thumb). Generally justified by the Central Limit Theorem Â¨ Â¤ Â© Âª Â«Â¬Â Â¹ Â®Â¯ Â° has approximately a standard normal distribution. Â± Â¤ Â²Â³Â´Â«Â Âµ Â¶ Â² Âº Â°Â®Â¸Â¶ is the test statistic. Case 3. The population is from the normal family with mean Â¬Â¥ . The sample size can be small but at least 2. Â» Â¤ Â© Âª Â«Â¬Â Â¼ Â®Â¯ Â° has a t distribution with df=n1 degrees of freedom Â½ Â¤ Â²Â³Â´Â«Â Âµ Â¶ Â² Âº Â°Â®Â¸Â¶ is the test statistic. Cases 1 and 2: The Distribution of the Test Statistic, Alternative Hypotheses and Rejection Regions for Â¡Â¢Â£ Â¤Â¥ : Alternative Hypothesis Rejection Region Standard Normal Distribution Â¦ Â§ Â¨ Â© Âª Â© Â« Â¬Â¢ Â Â¬ Â® Â¦ Â§ Â¨ Â© Â¯ Â© Â« Â¬Â¢ Â° Â±Â¬ Â® Â¦ Â§ Â¨ Â© Â² Â© Â« Â¬Â¢ Â° Â±Â¬ Â® Â³ Â´ Â¢ ÂµÂ¶ Â¢Â¬Â¢ Â Â¬ Â® Â³ Â´ Alpha is The probabilityof rejecting the null hypothesis when it is true ....
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This note was uploaded on 12/20/2011 for the course STAT 344 taught by Professor Staff during the Spring '08 term at George Mason.
 Spring '08
 Staff

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