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Behavioral Objectives for Business Statistics The student should be able… 1: Introduction and Data Collection 1. 2. 3. 4. 5. 6. To explain the difference between a sample and a population To explain the difference between a statistic and a parameter To explain the difference between descriptive and inferential statistics To identify categorical and numerical random variables To identify discrete and continuous data To explain the difference between various sampling schemes (random, stratified, cluster, etc) 7. To select a simple random sample 2: Presenting Data in Tables and Charts 8. To interpret frequency histograms, relative frequency histograms, scatterplots, bar charts, line (time series) charts, and pie charts 9. To identify deceptive graphic techniques, such as truncating the vertical axis or changing both the height and width of pictograms 3: Numerical Descriptive Measures 10. To compute and interpret measures of central tendency, variation and shape such as the mean, median, mode, range, standard deviation, variance, z-score, coefficient of variation, minimum, maximum, first quartile, third quartile and interquartile range 11. To state and apply the Empirical Rule for symmetric, unimodal distributions and Chebyshev’s theorem for non-symmetric distributions 12. To discuss conditions under which the median is preferred to the mean as a measure of central tendency, and vice versa 13. To describe the shape, center, and dispersion of a data set verbally, graphically, and/or numerically 4: Basic Probability 14. To define experiment, sample point, sample space, events, union, intersection, collectively exhaustive events, mutually exclusive events, independent events 15. To use contingency tables for joint probabilities 16. To compute and interpret conditional probability including the revision of prior probabilities using Bayes’ theorem (or contingency tables) 17. To apply the addition and multiplication rules of probability 1 5: Discrete Probability Distributions 18. To compute and interpret the expected value (mean), variance and standard deviation of a discrete random variable defined on a finite sample space 19. To identify binomial (and poisson) random variables and characterize their properties 20. To compute binomial (and poisson) probabilities 21. To compute the expected value, variance and standard deviation of a binomial (and poisson) random variable 22. To apply the binomial (and poisson) distribution to problems in business and economics 6: The Normal Distribution and Sampling Distributions The Normal Distribution 23. To identify normal random variables and characterize their properties 24. To compute probabilities for normal random variables using tables 25. To compute values of normal random variables for given probabilities 26. To assess the assumption of normality 27. To apply the normal distribution to problems in business and economics Sampling Distributions 28. To apply the concept of a sampling distribution 29. To compute the expected value and variance of a sample mean 30. To compute the sampling distribution for the mean of a sample from a normal population 31. To apply the Central Limit Theorem to derive the approximate sampling distribution for the mean of a sufficiently large sample from a non-normal population 32. To apply the Central Limit Theorem to derive the approximate sampling distribution (including the expected value and variance) for the proportion of successes in a sufficiently large sample 7: Confidence Interval Estimation 33. To interpret a confidence interval for a parameter 34. To construct a confidence interval for the mean when 2 is known 35. To construct a confidence interval for the mean when 2 is unknown 36. To construct a confidence interval for the proportion 37. To determine sample size for estimating a mean or proportion with a given level of confidence and bound on error of estimation 2 8: Fundamentals of Hypothesis Testing 38. To define alternative hypothesis, level of significance, null hypothesis, observed significance level (p-value), power of the test, rejection region, test statistic, Type I and Type II error 39. To explain the rationale of hypothesis testing 40. To test hypotheses about means and proportions using the steps of Hypothesis Testing with rejection regions and decision rules and sketch the power curve for a single mean hypothesis test. 41. To test hypotheses using computed p-values rather than rejection regions 42. To interpret the conclusions from a hypothesis test 9: Simple Linear Regression 43. To plot and interpret bivariate data as a scattergram with statistical software 44. To write a bivariate model and estimate the unknown parameters of the model from a data set using statistical software 45. To interpret the least squares estimates of the slope and intercept (if appropriate) 46. To state and understand the importance of the LINE regression assumptions within the context of a specific problem 47. To estimate the standard deviation of the probability distribution of the random error term 48. To statistically evaluate the usefulness of the model by testing H0 : 1 =0 49. To obtain and interpret a confidence interval estimate for the slope 50. To obtain and interpret Pearson's correlation coefficient and the coefficient of determination OPTIONAL 51. To obtain and interpret in context a confidence interval for the mean value of the dependent variable Y given a value of the independent variable X 52. To obtain and interpret in context a prediction interval for an individual value of the dependent variable Y given a value of the dependent variable X 53. To obtain and analyze residuals for impact on the estimated model coefficients and resulting predictions 3 4