LIR 832 midterm fall 2003 answer key

LIR 832 midterm fall 2003 answer key - LIR 832: Mid-term...

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LIR 832: Mid-term Examination: Fall, 2003 Answer all questions as completely as you are able. Partial credit on problems is only possible if I can locate arithmetic errors in your calculations. Show your work!!! Part I: Definitions: (20 points - 2 points per definition) Answer nine out of ten of the following. Provide a definition and explain the importance in statistics of each term. Do not limit yourself to copying the formulas from the formula sheet. I. 1% Test of Significance A 1% test of significance is a criteria which we use to determine whether the null is to be rejected. To perform this test we chose an appropriate z statistic, if our sample is greater than 30, or an appropriate t statistic, if our sample is 30 or smaller. If the z (or t value) produced by our sample is greater than the critical value, we reject the null. An interpretation of the test is that, if our null hypothesis is true, there is no more than a 1% likelihood that we will observe a value as extreme as the 1% critical value. Alternatively, if the null were true and we ran the experiment 100 times, we would expect a value in excess of the 1% critical value in 1 of the 100 tests. II. Experiment An act in which the outcome cannot be foretold with certainty. Most of life is made up of experiments. The potential outcomes of experiments have probabilities (or likelihoods) which indicate, ex ante, the chance that the particular outcome will occur. It is also the frequency with which we expect a given outcome will occur in a large number of repeated experiments. III. Z-transformation: The z-transform permits us to convert any normally distributed random variable into a standard normal random variable and thereby use the z-table to determine the probability of a particular outcome. IV. Sample Regression: Similar to what we learned with univariate statistics, there is a population regression which indicates the relationship between the explanatory and dependent variable for the entire group we would like to know about (the population). We estimate the population regression by taking a sample and estimating a sample regression. Similar to estimates of population means with samples, the sample regression is affected by sampling variability and does not exactly reproduce the population regression. Different samples will produce somewhat different coefficients.
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V. r 2 The coefficient of determination. is the ratio of the ESS/TSS or 1-RSS/TSS. It is a r 2 measure of the proportion of the variance of the dependent variable (movement of the dependent variable around its mean) which we can explain with our explanatory variables. VI. Representative Sample We use samples to learn about the characteristics of the populations which we are truely interested in but cannot observe. For a sample to be useful, it must be representative, it must reliably reproduce the characteristics of the population. For the most part, we use various forms of random sampling to produce representative samples. A problem with random sampling is that it is affecting by sampling variability VII.
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This note was uploaded on 07/25/2008 for the course LIR 832 taught by Professor Belman during the Spring '07 term at Michigan State University.

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LIR 832 midterm fall 2003 answer key - LIR 832: Mid-term...

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