Introduction to Statistics
Curriculum guideline
Lectures, group work, assignments.
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.
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)
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.
Consult the Douglas College bookstore for the current textbook. Sample textbooks:
Triola, Essentials of Statistics, Pearson, current edition
De Veaux et al, Stats: Data and Models, Pearson, current edition
Moore, Basic Practice of Statistics, Freeman, current edition
A calculator with statistical functionality may also be required.
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.