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# Introduction to Statistics

Course Code: MATH 1160
Faculty: Science & Technology
Department: Mathematics
Credits: 3.0
Semester: 15 weeks
Learning Format: Lecture, Tutorial
Typically Offered: Fall, Summer, Winter
course overview

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

### 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.
• Other probability distribtuions such as the uniform, geometric, and Poisson (optional).
• Mean and variance of linear combinations of independent random variables.

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 samples, estimating a population proportion.
• Determining a sample size.

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

• Computing and interpreting the meaning of the correlation coefficient and coefficient of determination.
• Constructing and applying linear models to make predictions.

### Methods of Instruction

Lectures, group work, assignments.

### 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.

### Learning Outcomes

At the end of the course, the successful student will 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
• Use the classical and relative frequency approaches to probability and counting techniques to solve problems
• 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
• Compute the mean and variance of a linear combination of independent random variables (optional)
• Determine probabilities of standard and non-standard normal random variables
• Use the Normal distribution to approximate Binomial probabilities
• Apply the Student t distribution
• Apply the Central Limit Theorem to estimate probabilities associated with sample spaces when the population is sufficiently large
• Perform hypothesis tests on population parameters or the difference between population parameters.
• 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)
• Apply Chebychev’s theorem (optional)
• Apply the Poisson and other probability distributions (optional)

course prerequisites

MATH 1105; 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.

curriculum guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester/year of the course, consider the previous version as the applicable version.

course schedule and availability
course transferability

Below shows how this course and its credits transfer within the BC transfer system.

A course is considered university-transferable (UT) if it transfers to at least one of the five research universities in British Columbia: University of British Columbia; University of British Columbia-Okanagan; Simon Fraser University; University of Victoria; and the University of Northern British Columbia.

For more information on transfer visit the BC Transfer Guide and BCCAT websites.

assessments