Download introduction - Warrior Run School District

WARRIOR RUN SCHOOL DISTRICT
WARRIOR RUN HIGH SCHOOL
MATH CURRICULUM
PROBABILITY AND STATISTICS
PREPARED BY:
MATH DEPARTMENT
SUBMITTED:
JUNE 2007
INTRODUCTION
Probability and Statistics is a course designed for students whose mathematical
background may be limited to basic algebra. A nontheoretical approach is used in
presenting the concepts. Applications of the material are general in nature and include
problems from all facets of life – business, economics, science, engineering and health
just to name a few.
Descriptive and inferential statistical techniques as well as probability theory are
discussed. Topics include numerical summary measures (mean, median, mode, variance
and standard deviation), graphing, standardized normal curve, counting techniques, rules
of probability and odds, common probability distributions and expected value.
EXPECTED LEVELS OF ACHIEVEMENT
Most students taking this course are college-bound seniors. A grade of 80%
overall is expected. Past experience indicates that students able to maintain 80% or better
are prepared to succeed in a college Probability and Statistics course. A list of
expectations follows:
The students are expected to:
 attain an average grade of 80% on all tests and quizzes.
 complete all homework assignments. Homework will be part of each nine
weeks’ average.
 master 80% of all written objectives as outlined in each unit of instruction.
 have a working knowledge of statistical concepts and probability which can
be applied in both the academic setting and in practical application in daily
living situations.
PROCEDURES FOR EVALUATION
Students will be evaluated using a variety of measurements. Grades will be
determined on a percentage basis as outlined in the teacher’s course description.
Evaluation will be based on the following:
1)
2)
3)
4)
Tests
Quizzes, announced and unannounced
Homework
Class participation
2
REFERENCES
Textbook: Elementary Statistics – A Step by Step Approach 4th Ed.
(Bluman)
TIMELINE
Unit 1
Counting Techniques
2 weeks
Unit 2
Probability
5 weeks
Unit 3
The Nature of Probability and Statistics
1 week
Unit 4
Frequency Distributions and Graphs
3 weeks
Unit 5
Data Description
6 weeks
Unit 6
Discrete Probability Distributions
4 weeks
Unit 7
The Normal Distribution
4 weeks
Unit 8
Correlation and Regression
4 weeks
Unit 9
Sampling
1 week
Unit 10
Statistics Project
3 weeks
Unit 11
Confidence Intervals and Sample Size
1.5 weeks
Unit 12
Hypothesis Testing
1.5 weeks
TOTAL:
36 weeks
*NOTE: Units 11 and 12 are optional and will be covered dependent
on time left at the end of the year.
3
UNIT 1
COUNTING TECHNIQUES
OBJECTIVES
Students will be able to:
1) determine the number of outcomes of a sequence of events using a tree diagram.
Std. 2.7.8.A
2) find the total number of outcomes in a sequence of events using the multiplication
rule of counting. Std. 2.7.8.A
3) find the number of ways r objects can be selected from n objects using the
permutation rule. Std. 2.7.8.A
4) find the number of ways r objects can be selected from n objects without regard to
order using the combination rule. Std. 2.7.8.A
CONTENT
1) Tree Diagrams and the Multiplication Rule for Counting (Obj. 1 and 2)
2) Permutations (Obj. 3)
3) Combinations (Obj. 4)
UNIT 2
PROBABILITY
OBJECTIVES
Students will be able to:
1) determine sample spaces and find the probability of an event using classical or
empirical probability. Std. 2.7.11
2) find the conditional probability of an event. Std. 2.7.11
3) find the probability of an event using the counting rules. Std. 2.7.11
4) find probabilities for independent, dependent or compound events and represent
as a fraction, decimal or percent. Std. 2.7.11.E
4
5) find, convert and/or compare the probability and/or odds of a simple event.
Std. 2.7.11.A
CONTENT
1) Sample Spaces and Probability (Obj. 1 and 5)
2) The Addition Rules of Probability (Obj. 4)
3) The Multiplication Rules and Conditional Probability (Obj. 2 and 4)
4) Probability and Counting Techniques (Obj. 3)
UNIT 3
THE NATURE OF PROBABILITY AND STATISTICS
OBJECTIVES
Students will be able to:
1) demonstrate knowledge of statistical terms. Std. 2.6.11
2) differentiate between the two branches of statistics. Std. 2.6.11
3) identify types of data. Std. 2.6.11
4) identify the measurement level for each variable. Std. 2.6.11
5) identify the four basic sampling techniques. Std. 2.6.11
6) explain the difference between an observational and an experimental study.
Std. 2.6.11
CONTENT
1) Descriptive and Inferential Statistics (Obj. 1 and 2)
2) Variables and Types of Data (Obj. 1, 3 and 4)
3) Data Collection and Sampling Techniques (Obj. 1 and 5)
5
4) Observational and Experimental Studies (Obj. 1 and 6)
UNIT 4
FREQUENCY DISTRIBUTIONS AND GRAPHS
OBJECTIVES
Students will be able to:
1) organize data using frequency distributions. Std. 2.6.11
2) represent data in frequency distributions graphically using histograms, frequency
polygons and ogives. Std. 2.6.11
3) represent data using Pareto charts, time series graphs and pie graphs. Std. 2.6.11
4) make predictions using data displays. Std. 2.6.11
CONTENT
1) Organizing Data (Obj. 1)
2) Histograms, Frequency Polygons and Ogives (Obj. 2 and 4)
3) Pareto Charts, Time Series Graphs and Pie Graphs (Obj. 3 and 4)
UNIT 5
DATA DESCRIPTION
OBJECTIVES
Students will be able to:
1) calculate or select the appropriate measure of central tendency (mean, median or
mode) of a set of data. Std. 2.6.11.A
2) describe data using the measures of variation, such as the range, variance and
standard deviation. Std. 2.6.11.A
6
3) calculate and/or interpret the range, quartiles and interquartile range of data.
Std. 2.6.11.A
4) describe how outliers affect measures of central tendency. Std. 2.6.11.A
5) identify the position of a data value in a data set using various measures of
position, such as percentiles, deciles and quartiles. Std. 2.6.11
6) create and/or use appropriate graphical representations of data, including box-and
-whisker plots, stem-and-leaf plots. Std. 2.6.8.E
7) analyze data and/or answer questions based on displayed data (box-and-whisker
plots and stem-and-leaf plots). Std. 2.6.8.E
8) determine five-number summaries for given set of data. Std. 2.6.11
CONTENT
1) Measures of Central Tendency (Obj. 1)
2) Measures of Variation (Obj. 2 and 3)
3) Measures of Position (Obj. 3, 4 and 5)
4) Five-Number Summaries, Box-and-Whisker Plots, and Stem-and-Leaf Plots
(Obj. 6, 7 and 8)
UNIT 6
DISCRETE PROBABILITY DISTRIBUTIONS
OBJECTIVES
Students will be able to:
1) construct a probability distribution for a random variable.
Stds. 2.6.11 and 2.7.11
2) find the mean, variance and expected value for a discrete random variable.
Std. 2.6.11
7
3) find the exact probability for X successes in n trials of a binomial experiment.
Std. 2.7.11
4) find the mean, variance and standard deviation for the variable of a binomial
distribution. Std. 2.6.11
5) find probabilities for outcomes of variables using the Poisson, hypergeometric,
and multinomial distributions. Std. 2.7.11
CONTENT
1) Probability Distributions
(Obj. 1)
2) Mean, Variance and Expectation (Obj. 2)
3) The Binomial Distribution (Obj. 3 and 4)
4) Poisson, Hypergeometric and Multinomial Distributions (Obj. 5)
UNIT 7
THE NORMAL DISTRIBUTION
OBJECTIVES
Students will be able to:
1) identify distributions as being symmetrical of skewed. Std. 2.6.11
2) identify the properties of the normal distribution. Std. 2.6.11.I
3) find the area under the standard normal distribution, given various z values.
Std. 2.6.11.I
4) find probabilities for a normally distributed variable by transforming it into a
standard normal variable. Std. 2.6.11.I
5) find specific data values for given percentages using the standard normal
distribution. Std. 2.6.11.I
6) use the central limit theorem to solve problems involving sample means for large
and small samples. Std. 2.6.11
8
7) use the normal approximation to compute probabilities for a binomial variable.
Std. 2.6.11.I
CONTENT
1) Properties of the Normal Distribution (Obj. 1 and 2)
2) The Standard Normal Distribution (Obj. 3)
3) Applications of the Normal Distribution (Obj. 4 and 5)
4) The Central Limit Theorem (Obj. 6)
5) The Normal Approximation to the Binomial Distribution (Obj. 7)
UNIT 8
CORRELATION AND REGRESSION
OBJECTIVES
Students will be able to:
1) create and/or use appropriate graphical representations of data. Std. 2.6.11.A
2) analyze data and/or answer questions based on displayed data. Std. 2.6.11.A
3) draw, find and/or write an equation for a line of best fit for a scatter plot.
Std. 2.6.11.C
4) make predictions using the equations or graphs of best-fit lines for scatter plots.
Std. 2.6.11.D
5) compute the correlation coefficient. Std. 2.6.11
6) compute the coefficient of determination and the standard error of estimate.
Std. 2.6.11
7) find a prediction interval. Std. 2.6.11
9
CONTENT
1) Scatter Plots (Obj. 1 and 2)
2) Correlation (Obj. 2)
3) Regression (Obj. 3 and 4)
4) Coefficient of Determination and Standard Error of Estimate (Obj. 5, 6, and 7)
UNIT 9
SAMPLING
OBJECTIVES
Students will be able to:
1) demonstrate a knowledge of the four basic sampling methods. Std. 2.6..8.B
2) recognize faulty questions on a survey and other factors that can bias responses.
Std. 2.6.8.B
3) determine the validity of the sampling method described in a given study.
Std. 2.6.11.E
CONTENT
1) Common Sampling Techniques (Obj. 1 and 3)
2) Surveys and Questionnaire Design (Obj. 2)
10
UNIT 10
STATISTICS PROJECT
OBJECTIVES
Students will be able to:
1) design and conduct an experiment using random sampling. Std. 2.6.11.A
2) describe the data as an example of a distribution using statistical measures of
center and spread. Std. 2.6.11.A
3) organize and represent the results of an experiment with graphs. Std. 2.6.11.A
4) use appropriate technology to organize and analyze data from an experiment
using random sampling. Std. 2.6.11.B
5) draw inferences about large populations using a random sample. Std. 2.6.11.H
CONTENT
1) Statistics Project Using a Random Sample (Obj. 1, 2, 3, 4 and 5)
UNIT 11
CONFIDENCE INTERVALS AND SAMPLE SIZE
OBJECTIVES
Students will be able to:
1) find the confidence interval for the mean when  is known or n  30.
Std. 2.6.11
2) determine the minimum sample size for finding a confidence interval for the
mean. Std. 2.6.11
3) find the confidence interval for the mean when  is unknown and n is less than
30. Std. 2.6.11
4) find the confidence interval for a proportion. Std. 2.6.11
11
5) determine the minimum sample size for finding a confidence interval for a
proportion. Std. 2.6.11
CONTENT
1) Confidence Intervals for the Mean and Sample Size (Obj. 1 and 2)
2) Confidence Intervals for the Mean (Obj. 3)
3) Confidence Intervals and Sample Size for Proportions (Obj. 4 and 5)
UNIT 12
HYPOTHESIS TESTING
OBJECTIVES
Students will be able to:
1) understand the definitions used in hypothesis testing. Std. 2.6.11
2) state the null and alternative hypotheses. Std. 2.6.11
3) find critical values for the z test. Std. 2.6.11
4) state the five steps used in hypothesis testing. Std. 2.6.11
5) test means for large samples using the z test. Std. 2.6.11
6) test means for small samples using the t test. Std. 2.6.11
7) test proportions using the z test. Std. 2.6.11
CONTENT
1) Steps in Hypothesis Testing-Traditional Method (Obj. 1, 2, 3 and 4)
2) Z-Test for a Mean (Obj. 5)
3) T-Test for a Mean (Obj. 6)
4) Z-Test for a Proportion (Obj. 7)
12