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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 2 Distribution t Distribution F Distribution 4 Confidence Intervals Introduction to CIs Normal Mean CIs (var known) Normal Mean CIs (var unknown) CIs for Other Parameters Goldsman 12/14/10 2 / 109 Descriptive Statistics Introduction to Statistics Statistics forms a rational basis for decisionmaking 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) Whats the most popular TV show during a certain time period? (6) The effect of various heattreating 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 cant 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 Its nice to have lots of data. But sometimes its 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 StemandLeaf 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. Propn of Range Freq. Freq. obsns so far 020 2 2 2/30 2140 5 7 7/30 4160 2 9 9/30 6180 10 19 19/30 81100 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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 Spring '07
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