MODULE 4 THE WHOLE MODULE

# MODULE 4 THE WHOLE MODULE - 4 Estimation Dave Goldsman...

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Unformatted text preview: 4. Estimation Dave Goldsman Georgia Institute of Technology, Atlanta, GA, USA 12/14/10 Goldsman 12/14/10 1 / 109 Outline 1 Descriptive Statistics 2 Point Estimation Intro to Estimation Unbiased Estimation Mean Squared Error Maximum Likelihood Estimation Method of Moments 3 Sampling Distributions Intro and Normal Distribution χ 2 Distribution t Distribution F Distribution 4 Confidence Intervals Introduction to CI’s Normal Mean CI’s (var known) Normal Mean CI’s (var unknown) CI’s for Other Parameters Goldsman 12/14/10 2 / 109 Descriptive Statistics Introduction to Statistics Statistics forms a rational basis for decision-making using observed or experimental data . We make these decisions in the face of uncertainty. Statistics helps us answer questions concerning: * The analysis of one population (or system) * The comparison of many populations. Goldsman 12/14/10 3 / 109 Descriptive Statistics Examples: (1) Election polling. (2) Coke vs. Pepsi. (3) The effect of cigarette smoking on the probability of getting cancer. (4) The effect of a new drug on the probability of contracting hepatitis. (5) What’s the most popular TV show during a certain time period? (6) The effect of various heat-treating methods on steel tensile strength. (7) Which fertilizers improve crop yield? (8) King of Siam — etc., etc., etc. Goldsman 12/14/10 4 / 109 Descriptive Statistics Idea (Election polling example): We can’t poll every single voter. Thus, we take a sample of data from the population of voters, and try to make a reasonable conclusion based on that sample. Statistics tells us how to conduct the sampling (i.e., how many observations to take, how to take them, etc.), and then how to draw conclusions from the sampled data. Types of Data: Continuous variables: Can take on any real value in a certain interval. For example, the lifetime of a lightbulb or the weight of a newborn child. Discrete variables: Can only take on specific values. For example, the number of accidents this week at a factory or the possible rolls of a pair of dice. Goldsman 12/14/10 5 / 109 Descriptive Statistics It’s nice to have lots of data. But sometimes it’s too much of a good thing! Need to summarize. Example: Grades on a test (i.e., raw data): 23 62 91 83 82 64 73 94 94 52 67 11 87 99 37 62 40 33 80 83 99 90 18 73 68 75 75 90 36 55 Goldsman 12/14/10 6 / 109 Descriptive Statistics Stem-and-Leaf Diagram of grades. Easy way to write down all of the data. Saves some space, and looks like a sideways histogram. 9 9944100 8 73320 7 5533 6 87422 5 52 4 3 763 2 3 1 81 Goldsman 12/14/10 7 / 109 Descriptive Statistics Grouped Data Cumul. Prop’n of Range Freq. Freq. obs’ns so far 0–20 2 2 2/30 21–40 5 7 7/30 41–60 2 9 9/30 61–80 10 19 19/30 81-100 11 30 1 Goldsman 12/14/10 8 / 109 Descriptive Statistics Summary Statistics: n = 30 observations If X i is the i th score, then the sample mean is ¯ X ≡ n X i =1 X i /n = 66 . 5 ....
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MODULE 4 THE WHOLE MODULE - 4 Estimation Dave Goldsman...

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