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Statistics 2014, Summer 2005 Final Exam Review Topics You will be allowed two 8.5” X 11” pages of notes. Chapter 1 – Statistics Statistics, Population, Sample, Parameter, Statistic, Variable, Data Branches of statistics: Descriptive, Inferential Types of data: 1) Attribute, or qualitative 2) Numerical, or quantitative Measurement scales: 1) Nominal, 2) Ordinal, 3) Interval/Ratio Representative sample Simple random sample of size n; how to select such a sample Systematic sample, Stratified random sample, Cluster sample Chapter 2 – Descriptive Analysis and Presentation of Single-Variable Data Categorical frequency distribution Grouped frequency distribution Class limits, widths, and midpoints Cumulative frequency, relative frequency, cumulative relative frequency Histogram, used with quantitative data Pareto chart, or bar graph, used with qualitative data Pie graph, used with qualitative data Measures of Central Tendency: 1) Mean, properties of mean; 2) Median, properties of median; 3) Mode, properties of mode Distribution shapes Symmetric: mean = median = mode Positively skewed: mode < median < mean Negatively skewed: mean < median < mode Which measure of central tendency is preferred, depending on shape of distribution and type of data. Measures of Variability: 1) Range, not the most useful; 2) Variance, more useful; 3) Standard Deviation, most useful (why?) Chebyshev’s Theorem Empirical Rule Measures of Position z-score, used for comparing scores from different data sets percentiles, locates position of a score relative to the rest of the data set quartiles interquartile range 5-number summary of a data set outliers Boxplots (box-and-whisker plots), information obtained from boxplot Stem-and-leaf plots, advantages and disadvantages Chapter 3 – Descriptive Analysis and Presentation of Bivariate Data 1) Two qualitative variables – contingency table 2) One qualitative and one quantitative variable – descriptive statistics and side-by-side boxplots 3) Two quantitative variables a) scatterplot to look for linear trend relationship b) Pearson correlation coefficient to measure direction and strength of linear trend c) regression equation and line of best fit to the data – predicting value of dependent variable for a given value of the independent variable Chapter 4 – Probability Random experiment; Sample space Events: 1) Simple event, 2) Compound event. Assigning probabilities to events: 1) Classical approach, 2) Relative frequency approach Mutually exclusive events Complement of an event -- Complement Rule Union of events, Intersection of events Basic Laws of Probability: 1) For any event A, 0 P(A) 1. 2) P(S) = 1. In other words, the outcome of the random experiment is certain to be in the sample space. 3) If two events A and B are mutually exclusive, then P( A B) P( A) P( B) . Addition Rule for Non-Mutually Exclusive Events Conditional probability and Independent events Multiplication Rule for independent events Chapter 5 – Probability Distributions Random variable Probability distribution, and Required properties of a probability distribution Expectation, or mean, of a probability distribution of a random variable X Variance of a random variable X Conditions for a binomial experiment Binomial probability distribution; binomial random variable X Finding binomial probabilities using the TI-83 Mean, variance and standard deviation for the Binomial Distribution Chapter 6 – The Normal Distribution Characteristics of normal distributions The Empirical Rule Standard Normal Distribution Finding normal probabilities using the TI-83 calculator Inverting the process: finding values of x (or z) corresponding to a particular probability Chapter 7 – Sample Variability Sampling error Sampling distribution of the mean; Properties of the sampling distribution of the mean Standard error of the mean The Central Limit Theorem Chapters 8 and 9 – Introduction to Statistical Inference Point estimator of a parameter Characteristics of a good estimator: 1) Unbiased, 2) Consistent, 3) Relatively efficient Confidence interval estimate: 1) Point estimate, 2) Width of interval, 3) Level of confidence T distribution and its characteristics How to find confidence interval for a population mean; interpretation of interval How to find confidence interval for a population proportion; interpretation of interval