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Statistics 2014, Fall 2014 Final Exam Review Topics Chapter 1 – Data Collection Statistics, Population, Sample, Parameter, Statistic, Variable, Data Branches of statistics: Descriptive, Inferential Types of data: 1) Attribute, or qualitative 2) Numerical, or quantitative (discrete or continuous) Representative sample v. census Simple random sample of size n; how to select such a sample Sampling error v. nonsampling error Designed experiment v. observational study; experimental unit, experimental treatment, response variable Chapter 2 – Organizing and Summarizing Data Categorical frequency distribution Grouped frequency distribution: Class limits, class width, cumulative frequency, relative frequency Histogram, used with quantitative data – Distribution shapes Pareto chart (bar graph), pie graph – both used with qualitative data Time series plot Chapter 3 – Numerically Summarizing 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?) Empirical Rule Measures of Position z-score, used for comparing scores from different data sets; what does a z-score mean? percentiles, locates position of a score relative to the rest of the data set; what does a percentile mean? quartiles interquartile range 5-number summary of a data set outliers Boxplots (box-and-whisker plots), information obtained from boxplot Chapter 4 – Describing the Relation between Two Variables Scatterplot to look for linear trend relationship, types of trends Pearson correlation coefficient to measure direction and strength of linear trend, properties of r Regression equation and line of best fit to the data – predicting value of dependent variable for a given value of the independent variable, interpreting the slope and intercept Chapter 5 – Probability Random experiment. Sample space Events: a) Simple event b) Compound event. Assigning probabilities to events: a) Classical approach b) Relative frequency (empirical) approach Interpreting a probability, in terms of relative frequency Mutually exclusive events Complement of an event – Complement Rule Union of events Intersection of events Basic Laws of Probability: (Kolmogorov’s Axioms): 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 Independent events Multiplication Rule for independent events Chapter 6 – Discrete Probability Distributions Random variables, discrete and continuous Probability distribution Required Properties of a Discrete Probability Distribution Expectation, or mean, of a probability distribution of a discrete random variable X. How to interpret the mean. Variance of a discrete random variable X Conditions for a binomial experiment Binomial probability distribution; binomial random variable X Finding binomial probabilities using the TI-83/TI-84 Mean, variance and standard deviation for the Binomial Distribution Chapter 7 – The Normal Probability Distribution Characteristics of normal distributions The Empirical Rule Standard Normal Distribution Finding normal probabilities using the TI-83/TI-84 calculator Inverting the process: finding values of x (or z) corresponding to a particular probability Chapter 8 – Sampling Distributions Sampling distribution of the sample mean Central Limit Theorem; finding approximate probabilities for the sample mean Chapter 9 – Estimating the Value of a Parameter Using Confidence Intervals Point estimator of a parameter Characteristics of a good estimator: 1) Unbiased, 2) Consistent, 3) Efficient Confidence interval estimate: 1) Point estimate, 2) Margin of Error, 3) Level of confidence How to interpret the level of confidence, in terms of relative frequency. How to find confidence interval for a population mean; interpretation of interval. How to find confidence interval for a population proportion; interpretation of interval. Chapter 10 – Hypothesis Tests Regarding a Parameter What is a hypothesis? Forms of hypothesis pairs Type I error, Type II error Significance level of test Test statistic for test about a population mean Test statistic for test about a population proportion Steps in hypothesis testing