Download Chapter 1 – Statistics

Statistics 2014, Summer 2005
Final Exam Review Topics
You will be allowed two 8.5” X 11” pages of notes.
Chapter 1 – Statistics
Statistics, Population, Sample, Parameter, Statistic, Variable, Data
Branches of statistics: Descriptive, Inferential
Types of data: 1) Attribute, or qualitative 2) Numerical, or quantitative
Measurement scales: 1) Nominal, 2) Ordinal, 3) Interval/Ratio
Representative sample
Simple random sample of size n; how to select such a sample
Systematic sample, Stratified random sample, Cluster sample
Chapter 2 – Descriptive Analysis and Presentation of Single-Variable Data
Categorical frequency distribution
Grouped frequency distribution
Class limits, widths, and midpoints
Cumulative frequency, relative frequency, cumulative relative frequency
Histogram, used with quantitative data
Pareto chart, or bar graph, used with qualitative data
Pie graph, used with qualitative data
Measures of Central Tendency: 1) Mean, properties of mean; 2) Median, properties of median; 3) Mode,
properties of mode
Distribution shapes
Symmetric: mean = median = mode
Positively skewed: mode < median < mean
Negatively skewed: mean < median < mode
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?)
Chebyshev’s Theorem
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
interquartile range
5-number summary of a data set
outliers
Boxplots (box-and-whisker plots), information obtained from boxplot
Stem-and-leaf plots, advantages and disadvantages
Chapter 3 – Descriptive Analysis and Presentation of Bivariate Data
1) Two qualitative variables – contingency table
2) One qualitative and one quantitative variable – descriptive statistics and side-by-side boxplots
3) Two quantitative variables
a) scatterplot to look for linear trend relationship
b) Pearson correlation coefficient to measure direction and strength of linear trend
c) regression equation and line of best fit to the data – predicting value of dependent variable for a
given value of the independent variable
Chapter 4 – Probability
Random experiment; Sample space
Events: 1) Simple event, 2) Compound event.
Assigning probabilities to events: 1) Classical approach, 2) Relative frequency approach
Mutually exclusive events
Complement of an event -- Complement Rule
Union of events, Intersection of events
Basic Laws of Probability:
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 and Independent events
Multiplication Rule for independent events
Chapter 5 – Probability Distributions
Random variable
Probability distribution, and Required properties of a probability distribution
Expectation, or mean, of a probability distribution of a random variable X
Variance of a 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 6 – The Normal 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 7 – Sample Variability
Sampling error
Sampling distribution of the mean; Properties of the sampling distribution of the mean
Standard error of the mean
The Central Limit Theorem
Chapters 8 and 9 – Introduction to Statistical Inference
Point estimator of a parameter
Characteristics of a good estimator: 1) Unbiased, 2) Consistent, 3) Relatively efficient
Confidence interval estimate: 1) Point estimate, 2) Width of interval, 3) Level of confidence
T distribution and its characteristics
How to find confidence interval for a population mean; interpretation of interval
How to find confidence interval for a population proportion; interpretation of interval