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Midterm exam Thursday, March 14, 2002 Regular class time You may bring one 8.5 by 11 sheet with anything on it that you wish. You may use calculators. List of topics Summary statistics Parameter estimation Mean Sample variance and sample standard deviation Median Quantiles Interquartile range (IQR) Extremes (maximum, minimum) Method of moments Maximum likelihood Unbiased estimator Estimation of mean, variance and standard deviation Standard error Confidence interval Graphical summaries Hypothesis tests Histogram Box and whiskers plot Scatter plot Quantile-quantile plot Null hypothesis Alternative hypothesis Test statistic p-value Significance level Critical value Rejection region Power Power curve t-statistic (hypothesis about mean) Generalized likelihood ratio statistic Chisquare approximation Sampling Simple random sampling Stratified sampling Population Population mean and variance Parametric models Normal distribution Lognormal distribution Poisson distribution Exponential distribution Gamma distribution Uniform distribution Binomial and multinomial distributions Possible types of questions Given a list of formulas for statistics and other quantities we have discussed and a list of statements about statistics and other quantities, match the correct formula or formulas to each statement. For a specified collection of objects, people, or some other unit, describe a good way to use sampling to estimate the average value of some quantity of interest. How would you select your sample? How would you compute the estimate? How would you indicate the accuracy of your estimate? How would you interpret a given plot? What can you say about the underlying distribution of the data? For a parametric family of distributions, how would you derive reasonable estimators for the parameters? How would you indicate the accuracy of your estimates? How could you check whether or not this parametric family provides a good model for the data? Given values of summary statistics (e.g., sample mean and variance), compute the value of your estimate or a confidence interval. Given a scientific question, describe how to set up a hypothesis test that addresses the question. What are the null and alternative hypotheses? What is the form of the rejection region? How would you compute the p-value? For a given significance level, how would you find the critical value?