Download STA-3111: Statistics I Text Book: McClave and Sincich, 12th edition

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
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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
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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
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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
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(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