Review Topics for Final Exam

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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.

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