Statistics 2014, Fall 2014
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 v. observational study; 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
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: 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?)
Empirical Rule
Measures of Position
z-score, used for comparing scores from different data sets; what does a z-score mean?
percentiles, locates position of a score relative to the rest of the data set; what does a percentile mean?
quartiles
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 Variables
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.
Sample space
Events: a) Simple event
b) Compound event.
Assigning probabilities to events: a) Classical approach b) Relative frequency (empirical) approach
Interpreting a probability, in terms of relative frequency
Mutually exclusive events
Complement of an event – Complement Rule
Union of events
Intersection 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
Multiplication Rule for independent events
Chapter 6 – Discrete 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. How to interpret 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/TI-84
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/TI-84 calculator
Inverting the process: finding values of x (or z) corresponding to a particular probability
Chapter 8 – Sampling Distributions
Sampling distribution of the sample mean
Central Limit Theorem; finding approximate probabilities for the sample mean
Chapter 9 – Estimating the Value of a Parameter Using Confidence Intervals
Point estimator of a parameter
Characteristics of a good estimator: 1) Unbiased, 2) Consistent, 3) Efficient
Confidence interval estimate: 1) Point estimate, 2) Margin of Error, 3) Level of confidence
How to interpret the level of confidence, in terms of relative frequency.
How to find confidence interval for a population mean; interpretation of interval.
How to find confidence interval for a population proportion; interpretation of interval.
Chapter 10 – Hypothesis Tests Regarding a Parameter
What is a hypothesis?
Forms of hypothesis pairs
Type I error, Type II error
Significance level of test
Test statistic for test about a population mean
Test statistic for test about a population proportion
Steps in hypothesis testing