# Introduction to Statistics

## Curriculum Guideline

Effective Date:
Course
Discontinued
No
Course Code
MATH 1160
Descriptive
Introduction to Statistics
Department
Mathematics
Faculty
Science & Technology
Credits
3.00
Start Date
End Term
201810
PLAR
No
Semester Length
15 weeks
Max Class Size
35
Contact Hours
4 hours lecture and 1 hour tutorial
Method Of Instruction
Lecture
Tutorial
Methods Of Instruction

Lectures, group work, assignments.

Course Description
A pre-calculus introduction to descriptive statistics, measures of central tendency and variation, elementary probability, probability distributions, sampling, hypothesis testing, regression, correlation and chi-square testing.
Course Content

Introduction to Statistics

• The nature of data, uses and abuses of statistics, design of experiments statistics with calculator and computers.

Describing exploring and comparing data

• Summarizing data with frequency tables, pictures of data, measures of central tendency, measures of variation, measures of position, exploratory data analysis.

Probability

• Definitions, addition rule, multiplication rule, probabilities through simulation, counting.

Probability Distributions

• Random variables, binomial experiments, mean, variance and standard deviation for the Binomial distribution.

Normal Probability Distributions

• The Standard Normal distribution, non-standard Normal distributions, the Central Limit Theorem, Normal approximation to the Binomial distribution.

Estimates and Sample Sizes

• Estimating a population mean using large and small samples, estimating a population proportion.

Hypothesis Testing

• Fundamentals of Hypothesis Testing, testing a claim about a mean using large and small samples, testing a claim about a proportion.
• Confidence intervals.

Inferences from Two Samples

• Inferences about two means: dependent samples, inferences about two means: independent and large samples, inferences about two means: independent and small samples, inferences about two proportions

Correlation and Regression

• Correlation, regression variation
Learning Outcomes

At the end of the course, the successful student should be able to:

•  Define the terms “population” and “sample” as they apply to Statistics
• Define and differentiate between the nominal, ordinal, interval and ratio levels of measurement
• Explain the proper use of Statistics within real world application and provide examples of its abuse
• Have an understanding of experimental design and the use of random number tables and generators
• Create and interpret frequency tables, histograms, cumulative frequency tables, stem and leaf displays and scatter plots
• Calculate and interpret measures of central tendency and variation
• Calculate and interpret standard scores
• Understand the classical and relative frequency approaches to probability and employ counting techniques
• Know and apply the addition and multiplication rules for probability and the concept of conditional probability
• Be able to differentiate between discrete and continuous random variables
• Determine whether the conditions for a Binomial experiment apply and compute the Binomial probabilities
• Compute the mean, variance and standard deviation for the Binomial distribution
• Determine probabilities of standard and non-standard normal random variables
• Use the Normal distribution to approximate Binomial probabilities
• Understand and apply the Student t distribution
• Apply the Central Limit Theorem to estimate population parameters using large and small samples
• Apply the Central Limit Theorem to estimate the difference between population parameters
• Perform hypothesis tests on population parameters or the difference between population parameters using large and small samples
• Create confidence intervals for population parameters or their difference using large and small samples.
• Create Contingency Tables and perform goodness-of-fit testing in multinomial experiments using the Chi-square test. (optional)
• Understand and apply Chebychev’s theorem (optional)
• Understand and apply the Poisson and other probability distributions (optional)
Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy.  The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester.  Evaluation will be based on some of the following:

 Weekly quizzes 0-20% Term tests 20-70% Tutorials 0-10% Participation/attendance 0-5% Assignments 0-10% Final exam 30-40%

Note:  Students may be required to pass the final exam in order to be eligible to pass the course.

Textbook Materials

Textbooks and Materials to be Purchased by Students

• Moore, The Basic Practice of Statistics, current edition, Freeman
• Calculator TI83+ or TI84 (optional)
Prerequisites

Math 1105; or B.C. Principles of Math 11 with a B or better; or B.C. Applications of Math 11 with an A- or better; or B.C. Principles of Math 12 with a C or better; or B.C. Applications of Math 12 with a B or better; or Precalculus 11 with a B or better; or Precalculus 12 with a C or better; or Foundations of Math 11 with a B or better; or Foundations of Math 12 with a C or better.