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112_hanouts_weeks_1-2_W_07 - Statistics 112 Session One...

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Statistics 112 Session One Professor Esfandiari Winter 2007 I The objective of this lecture is to A. Make you familiar with the following terms: Data: The information gathered from data and experiments 1. Statistics: The art and science of learning from data 2. Main aspects of statistics including a) Design: Planning how to collect data to answer question of interest b) Description: Summarizing data that are obtained c) Inference: Making decisions and descriptions based on data 3. Sample: Subset of the population on which we collect data 4. Population: Total subjects we are interested in 5. Subject: The entities that we measure in a study 6. Descriptive statistics: Using graphical and numerical summaries to describe a sample 7. Inferential statistics: Using the data from the sample to make inference about the 8. Population 9. statistic: Numerical summary for the population 10. Sample: Numerical summary for the sample B. Importance of random sampling in choosing a representative sample form the population and designing experiments C. The role of computers and a sample data file Some basic definitions Population : Population includes all the potential elements that could be part of a study. Population could be finite; i.e. we know how many elements are included in the population. Population could be infinite ; we do not know how many elements are included in the population. Examples of finite populations : All the high school students in the United States. All of the students who major in political science in state universities in the United States. Examples of infinite populations: The number of pebbles in a certain beach. The number of trees in a certain jungle, etc. Samples are a fraction of the population and we already discussed methods of choosing unbiased and representative samples. Parameters are used to describe a population. Statistics are used to describe a sample.
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Descriptive statistics relates to describing the sample . So, calculating the mean, median, mode, variance, standard deviation, and correlation for a sample of size n are examples of descriptive statistics. Inferential statistics is about generalizing the results from the sample to the population. For example, when we make a statement such as; "We are 95% confident that this drug lowers blood pressure between 10 to 20 points", we are not making this statement about a sample of size n. We are implying that these results are true for the population of individuals who have high blood pressure. Thus, we are generalizing the findings from the sample of size n to the population. Symbols used to show parameters and statistics Index Symbol used to show statistic in the ample Symbols used to show parameter in the population Mean X μ Percentage P^ (hat shows estimate) P Variance S^2 ^2 σ Standard deviation S σ Correlation r μ For clarification of part A, the following problems will be discussed To explain concepts 1-2, you will read and analyze scenarios 1-3 on pages 5-6.
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112_hanouts_weeks_1-2_W_07 - Statistics 112 Session One...

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