Statistics 2014, Summer 2013
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, 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, cumulative 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: Mean, Median, Mode; properties of Mean, Median, Mode
Distribution shapes and relationships among measures of central tendency
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 percentiles, locates position of a score relative to the rest of the data set quartiles and 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 Variable
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, and sample space
Events: Simple event, Compound event.
Assigning probabilities to events: a) Classical approach, b) Relative frequency (empirical) approach
Interpreting a probability
Mutually exclusive events
Complement of an event – Complement Rule
Unions and intersections 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 and Multiplication Rule for independent events
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. Interpreting 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
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 calculator
Inverting the process: finding values of x (or z) corresponding to a particular probability
Chapter 8 – Sampling Distributions and the Central Limit Theorem
Sampling distribution of the sample mean
Central Limit Theorem; finding approximate probabilities for the sample mean
Sampling distribution of the sample proportion
Finding approximate probabilities for the sample proportion
Chapter 9 – Confidence Intervals and Sample Size
Point estimator of a parameter
Confidence interval estimate: 1) Point estimate, 2) Width of interval, 3) Level of confidence
How to find confidence interval for a population mean.
How to find confidence interval for a population proportion.