Download Chapter 6 – Probability Distributions

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