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Statistics 2023, Fall 2008 Final Exam Review Topics You will be allowed two 8.5” X 11” pages of notes. Chapter 1 – What is Statistics Statistics, Population, Sample Branches of statistics: Descriptive, Inferential Types of data: 1) Attribute, or qualitative 2) Numerical, or quantitative (discrete or continuous) Sampling: Why do we do sampling? Representative sample. Nominal, Ordinal, Interval-ratio levels of measurement Chapter 2 – Descibing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation Frequency table for qualitative data Bar graph, pie graph – both used with qualitative data Grouped frequency distribution for quantitative data: “2 to the k rule,” class limits, class width, cumulative frequency, relative frequency, cumulative relative frequency Histogram, used with quantitative data – Distribution shapes Frequency polygon, cumulative frequency distribuition Chapter 3 – Describing Data: Numerical Measures Arithmetic mean, weighted mean, median, mode, geometric mean Which measure of central tendency is preferred, depending on shape of distribution and type of data. Distribution shapes Symmetric: mean = median = mode Positively skewed: mode < median < mean Negatively skewed: mean < median < mode Measures of Variability: 1) Range, not the most useful; 2) Variance, more useful; 3) Standard Deviation, most useful (why?) Chebyshev’s Inequality Empirical Rule Arithmetic mean and standard deviation for grouped data Chapter 4 – Describing Data: Displaying and Exploring Data Dotplots, stem-and-leaf plots Percentiles, quartiles, deciles, IQR Boxplots Coefficient of skewness Scatterplot to look for linear trend relationship, types of trends Contingency tables Chapter 5 – A Survey of Probability Concepts Random experiment. Sample space Events; outcomes Assigning probabilities to events: a) Classical approach b) Empirical approach Mutually exclusive events Complement of an event – Complement Rule Union of events Intersection of events Addition Rule Conditional Probability Independent events Multiplication Rule for independent events Tree diagram Bayes’ Theorem c) Subjective approach Chapter 6 – 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. 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, or using the table in the Appendix Mean, variance and standard deviation for the Binomial Distribution Chapter 7 – The Normal Probability Distribution Uniform distribution; probabilities, mean, standard deviation Characteristics of normal distributions Standard Normal Distribution Empirical Rule Finding normal probabilities using the TI-83 calculator, or using the table in the Appendix Chapter 8 – Sampling Methods and the Central Limit Theorem Why we do sampling Sampling methods: 1) Simple random sampling, 2) Systematic sampling, 3) Stratified random sampling, 4) Cluster sampling Sampling distribution of the sample mean Central Limit Theorem; finding approximate probabilities that the sample mean is within certain intervals Chapter 9 – Estimation and Confidence Intervals Point estimator of a parameter Level of confidence Confidence interval estimate: 1) Point estimate, 2) Width of interval, 3) Level of confidence How to find confidence interval for a population mean; interpretation of interval. How to find confidence interval for a population proportion; interpretation of interval. How to decide on the size of the sample so that a desired margin of error is achieved with a desired level of confidence Chapter 10 – One-Sample Tests of Hypotheses What is a hypothesis? Forms of hypothesis pairs Type I error, Type II error Significance level of test Steps in hypothesis testing Tests of hypotheses about a population mean Tests of hypotheses about a population proportion