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STA-3111: Statistics I Text Book: McClave and Sincich, 12th edition Contents and Objectives Chapters 1 – 8 (Revised: Aug. 2014) Chapter 1: Nature of Statistics and its Methods (all sections) Descriptive statistics Inferential statistics Basic concepts in inferential statistics Population Census Sample Representative sample Simple random sampling Sampling survey Inferential statistics scheme Role of probability in inferential statistics Individuals, variables, and data Types of data: qualitative (categorical) and quantitative. Examples Chapter 2: Descriptive Statistics (sections 2.1-2.8) Organizing data: frequency tables and graphs Frequency graphs for categorical data: bargraphs and piecharts Frequency graphs for quantitative data: histograms and stem and leaf diagrams Measures of central tendency: mean, median, mode Frequency curves. Special cases Comparing the measures of center for grouped data Measures of variability or spread: range, variance and standard deviation Outliers. Effect of outliers on the measures of center and spread Use of the calculator’s statistical functions for the computation of the sample mean and standard deviation Chebyshev and Empirical rules Measures of relative standing: percentiles and quartiles Describing the center and spread of a data set with a Five Number Summary and Box Plot Detecting outliers using the Five Number Summary and Box Plot. Calculating fences. Chapter 3: Probability (sections 3.1 - 3.6) Basic concepts in probability Random experiment Sample space Sample points Event Impossible event Certain event Venn diagram General probability model: assumptions Assigning probabilities to events Equally likely sample points Not equally likely sample points Compound events: Intersection, Union, and Complement Mutually exclusive events Conditional probability: computation and interpretation Independent events Probability Rules Addition Complement Multiplication Conditional Computing probabilities using a: Venn diagram Contingency table Probability tree Chapter 4: Discrete Random Variables (sections 4.1 - 4.4) Basic concepts Random variable Discrete and continuous random variables Discrete probability distribution A. Discrete Probability Distributions Properties of a discrete probability distribution Discrete probability tables Discrete probability graphs: bar graphs and point graphs Computing and interpreting probabilities of events involving a discrete random variable Mean of a discrete random variable. Computation and interpretation Standard deviation of a discrete random variable. Computation and interpretation B. Binomial Probability Distribution Binomial experiment Binomial variable Parameters: number of trials (n) and expected rate of success (p) Binomial probability formula Binomial probability table Word problems involving probabilities on a Binomial variable Mean and standard deviation Chapter 5: Continuous Random Variables (sections 5.1 & 5.3) Basic Concepts Continuous random variable Normal random variable Normal curve Normal population Normal probability distribution. Parameters Normal Probability Distribution Properties of the normal curve Graphing normal curves Interpreting the areas under the Normal curve Empirical rule Standard Normal Distribution Computing and interpreting z-scores Properties of the Standard Normal Curve (SNC) Use of the Standard Normal Table (z-table): (1) Finding areas/probab (2) Finding z-scores Applications Areas under any normal curve Solving word problems Chapter 6: Sampling Distributions (sections 6.1 - 6.3) Basic Concepts in Inferential Statistics Inferential statistics scheme Population Sample Representative sample Sampling techniques Simple random sampling Statistical inference Parameter Statistic Sampling distribution Sampling distribution of the sample mean Properties: mean and standard deviation Central Limit Theorem Maximum sampling error Sampling distribution of the sample proportion Properties: mean and standard deviation Chapter 7: Estimation with Confidence Intervals (sections 7.1 - 7.4) Basic concepts in estimation Estimation Estimator Point estimates Interval estimates Margin of error Confidence coefficient/level Confidence interval Precision Effect of the confidence level and sample size on the precision of the estimates. Computing and interpreting confidence intervals for a population mean. Large sample size/Use of the z-table Small sample size/Use of the t-table Computing and interpreting confidence intervals for a population proportion using a large sample. Chapter 8: Hypothesis Testing based on a single sample (sections 8.1 - 8.6) Basic elements of hypothesis testing Research hypothesis Statistical hypotheses: null and alternative Test statistic (TS) Rejection region (RR). Location and critical values Type I and II errors/Probabilities Alpha and Beta Significance level of the test P-values Interpreting p-values Computing p-values with the z-table Two approaches for testing hypotheses Traditional: TS & RR Alternate: p-value & significance level Conducting tests of hypotheses about a (1) (2) (3) Population mean using a large sample: z-test Population mean using a small sample: t-test Population proportion using a large sample: z-test