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Lecture09

# Lecture09 - STAT 350 LECTURE 9 Chapter 5(5.5 Sample...

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STAT 350 L ECTURE 9 Chapter 5 (5.5) Sample Distributions

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S TATISTICAL I NFERENCE What is it? Generalize from the samples to the population Use statistics to make statement about population parameters Specify the likelihood of the statement being right What is it based on? Random Samples (e.g. SRS) Sampling Distributions (Focus of this lecture) Probability
40 R ANDOM S AMPLES Scenario: We would like to find out the number of hours per week that Purdue students spent on their homework (denoted as x) Recruited 40 interviewers Randomly selected 100 Purdue students for each interviewer 40 Simple Random Samples, independent of each other Each investigator will take a SRS, and interview the 100 students on their workload.. How many datasets do we have? What is the content of each dataset?

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40 D ATASETS Dataset 1: 20, 15, 18, 10,22, 17, etc… Dataset 2: 12, 28, 14, 19, 25, 25, etc… A total of 40 datasets with different content Sample Means: Dataset 1: Dataset 2: 40 sample means x 1 x 2 x 1 , x 2 , x 3 , x 4 ,,..., x 39 , x 40 ,
40 S AMPLE M EANS A total of 40 datasets with different content 40 sample means Plot Histogram for the 40 sample means The sample mean (a statistic) is random with its own distribution x 1 , x 2 , x 3 , x 4 ,,..., x 39 , x 40 ,

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S AMPLING D ISTRIBUTIONS Definition: The Sampling Distribution of a statistic is a mass or density function that characterizes all
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