# MS 150 Statistics

This outline is under redevelopment. This document includes multiple presentations and comments which will eventually be removed from the final document.

Course Description: This is a semester course designed as an introduction to the basic ideas of data presentation, descriptive statistics, basic probability, and inferential statistics. The course incorporates the use of a computer spreadsheet package, Microsoft Excel, for both data analysis and presentation. Basic concepts are studied using applications from business, social science, health science, and the natural sciences.

Hours per week: 3
Number of weeks: 16
Semester credits: 3
Prerequisite course: MS 100 College Algebra

## Strictly Mapped Format

1. Program Outcomes
Students will be able to:
1. define arithmetic, algebraic, geometric, spatial, and statistical concepts
2. calculate arithmetic, algebraic, geometric, spatial, and statistical quantities using appropriate technology.
3. estimate arithmetic, algebraic, geometric, spatial, and statistical solutions
4. solve arithmetic, algebraic, geometric, spatial, and statistical expressions, equations, functions, and problems using appropriate technology.
5. represent mathematical information numerically, symbolically, graphically, verbally, and visually using appropriate technology.
6. develop mathematical and statistical models such as formulas, functions, graphs, tables, and schematics using appropriate technology.
7. interpret mathematical and statistical models such as formulas, functions, graphs, tables, and schematics, drawing conclusions and making inferences based on those models.
8. explore mathematical systems utilizing rich experiences that encourage independent, nontrivial, constructive exploration in mathematics.
9. communicate mathematical thoughts and ideas clearly and concisely to others in the oral and written form.
2. Course Outcomes

#### Students will be able to:

1. define statistical concepts
1. [Core] Identify the shape of a distribution as being symmetrical, uniform, bimodal, skewed right, skewed left, or normally symmetric.
2. [Peri] Distinguish between a population and a sample
3. [Peri] Distinguish between a statistic and a parameter
4. [Peri] Identify by characteristics normal curves from a set of normal and non-normal graphs of lines.
5. [Peri] Identify different levels of measurement when presented with nominal, ordinal, interval, and ratio data.
6. [Core] Identify the sign of a least squares line: positive, negative, or zero.
2. calculate statistical quantities using appropriate technology.

Given one variable data and the use of a calculator or spreadsheet software on a computer

1. [Core] Determine a sample size
2. [Core] Determine a sample minimum
3. [Core] Determine a sample maximum
4. [Core] Calculate a sample range
5. [Core] Determine a sample mode
6. [Core] Determine a sample median
7. [Core] Calculate a sample mean
8. [Core] Calculate a sample standard deviation
9. [Core] Calculate a sample coefficient of variation
10. [Core] Calculate a class width given a number of desired classes
11. [Core] Determine class upper limits based on the sample minimum and class width
12. [Core] Calculate the frequencies
13. [Core] Calculate the relative frequencies (probabilities)
14. [Core] Determine a point estimate for the population mean based on the sample mean
15. [Core] Calculate a t-critical value from a confidence level and the sample size
16. [Core] Calculate an error tolerance from a t-critical, a sample standard deviation, and a sample size.
17. [Core] Calculate the two-tailed p-value using a sample mean, sample standard deviation, sample size, and expected population mean to to generate a t-statistic.

Given two variable data and the use of spreadsheet software on a computer

18. [Core] Calculate the slope of the least squares line.
19. [Core] Calculate the intercept of the least squares line.
20. [Core] Calculate the correlation coefficient r.
21. [Core] Calculate the coefficient of determination r².
3. estimate statistical solutions

Given one variable data and the use of spreadsheet software on a computer

1. [Peri] Estimate a mean from class upper limits and relative frequencies using the formula Sx*P(x) here the probability P(x) is the relative frequency.
4. solve statistical problems using appropriate technology.

Given one variable data and the use of spreadsheet software on a computer

1. [Core] Solve for a confidence interval based on a confidence level, the associated t-critical, a sample standard deviation, and a sample size where the sample size is less than 30.

Given two variable data and the use of spreadsheet software on a computer

2. [Core] Solve for a y value given an x value and the slope and intercept of a least squares line.
3. [Core] Solve for a x value given an y value and the slope and intercept of a least squares line.
5. represent mathematical information numerically, symbolically, graphically, verbally, and visually using appropriate technology.

Given one variable data and the use of spreadsheet software on a computer

1. [Peri] create a frequency histogram based on calculated class widths and frequencies
2. [Core] create a relative frequency histogram based on calculated class widths and frequencies
6. develop mathematical and statistical models such as formulas, functions, graphs, tables, and schematics using appropriate technology.
1. Discover the normal curve through a course-wide effort involving tossing seven pennies and generating a histogram from the in-class experiment.
7. interpret statistical models such as formulas, functions, graphs, tables, and schematics, drawing conclusions and making inferences based on those models.

Given one variable data and the use of spreadsheet software on a computer

1. [Core] Use a confidence interval to determine if the mean of a new sample places the new data within the confidence interval or is statistically significantly different.
2. [Peri] Infer from a p-value the largest confidence interval for which a change is not significant.

Given two variable data and the use of spreadsheet software on a computer

3. [Core] Use a correlation coefficient r to render a judgment as to whether a correlation is perfect, high, moderate, low, or none.
8. explore mathematical systems utilizing rich experiences that encourage independent, nontrivial, constructive exploration in mathematics.
9. communicate mathematical thoughts and ideas clearly and concisely to others in the oral and written form.

### Instructor Intentions

• Use of Microsoft Excel and Microsoft Excel functions throughout the course as opposed to using dedicated statistics software package. Excel and other spreadsheets will be the desktop software most widely available to MS 150 students both while taking the course and, more importantly, in the workplace post-graduation.
• Use of real-world data, examples, and problems to the extent appropriate and possible.

### Assessment

Assessment will be via quizzes, tests, midterm examinations and a final examination. All core outcomes will appear on the final examination.

### Notes

[Core] outcomes are tested on the cumulative final examination and preceding quizzes, tests, and midterm examinations. Students must successfully achieve core outcomes in order to pass the class.

[Peri] outcomes are tested during the course and may appear on the final. Their achievement is used to distinguish levels of skill above a minimal pass.

Note that the course has modified the program outcomes to those sectors pertinent to the course in the course outcomes.

In the final outline the last two program outcomes would be deleted as no course outcome meets those program outcomes. These two program outcomes have been left in this outline for informational purposes. This is one of the first outlines in the division to be rewritten in this format.

The complication is that the resulting outline is difficult to read: the material is not in topical order nor in any form of chronological order. One cannot at a glance see all of the outcomes related to a particular topic. The result is a choppy and disorganized document that says more about particular program skills attained than the actual coverage of the course.

## Topical with reference mapping

1. Program Outcomes
Students will be able to:
1. define arithmetic, algebraic, geometric, spatial, and statistical concepts
2. calculate arithmetic, algebraic, geometric, spatial, and statistical quantities using appropriate technology.
3. estimate arithmetic, algebraic, geometric, spatial, and statistical solutions
4. solve arithmetic, algebraic, geometric, spatial, and statistical expressions, equations, functions, and problems using appropriate technology.
5. represent mathematical information numerically, symbolically, graphically, verbally, and visually using appropriate technology.
6. develop mathematical and statistical models such as formulas, functions, graphs, tables, and schematics using appropriate technology.
7. interpret mathematical and statistical models such as formulas, functions, graphs, tables, and schematics, drawing conclusions and making inferences based on those models.
8. explore mathematical systems utilizing rich experiences that encourage independent, nontrivial, constructive exploration in mathematics.
9. communicate mathematical thoughts and ideas clearly and concisely to others in the oral and written form.
2. Course Outcomes
Students will be able to:

Given one variable data and the use of a calculator or spreadsheet software on a computer

Basic Statistics
1. [Peri] Distinguish between a population and a sample (Define)
2. [Peri] Distinguish between a statistic and a parameter (Define)
3. [Peri] Identify different levels of measurement when presented with nominal, ordinal, interval, and ratio data. (Define)
4. [Core] Determine a sample size (calculate)
5. [Core] Determine a sample minimum (calculate)
6. [Core] Determine a sample maximum (calculate)
7. [Core] Calculate a sample range (calculate)
8. [Core] Determine a sample mode (calculate)
9. [Core] Determine a sample median (calculate)
10. [Core] Calculate a sample mean (calculate)
11. [Core] Calculate a sample standard deviation (calculate)
12. [Core] Calculate a sample coefficient of variation (calculate)

13. Histograms
14. [Core] Calculate a class width given a number of desired classes (calculate)
15. [Core] Determine class upper limits based on the sample minimum and class width (calculate)
16. [Core] Calculate the frequencies (calculate)
17. [Core] Calculate the relative frequencies (probabilities) (calculate)
18. [Peri] create a frequency histogram based on calculated class widths and frequencies (represent)
19. [Core] create a relative frequency histogram based on calculated class widths and frequencies (represent)
20. [Core] Identify the shape of a distribution as being symmetrical, uniform, bimodal, skewed right, skewed left, or normally symmetric. (Define)
21. [Peri] Estimate a mean from class upper limits and relative frequencies using the formula Sx*P(x) here the probability P(x) is the relative frequency. (estimate)

22. Normal Curves and Confidence Intervals
23. Discover the normal curve through a course-wide effort involving tossing seven pennies and generating a histogram from the in-class experiment. (develop)
24. [Peri] Identify by characteristics normal curves from a set of normal and non-normal graphs of lines. (Define)
25. [Core] Determine a point estimate for the population mean based on the sample mean (calculate)
26. [Core] Calculate a t-critical value from a confidence level and the sample size (calculate)
27. [Core] Calculate an error tolerance from a t-critical, a sample standard deviation, and a sample size. (calculate)
28. [Core] Solve for a confidence interval based on a confidence level, the associated t-critical, a sample standard deviation, and a sample size where the sample size is less than 30. (solve)
29. [Core] Use a confidence interval to determine if the mean of a new sample places the new data within the confidence interval or is statistically significantly different. (interpret)

30. P-Values
31. [Core] Calculate the two-tailed p-value using a sample mean, sample standard deviation, sample size, and expected population mean to to generate a t-statistic. (calculate)
32. [Peri] Infer from a p-value the largest confidence interval for which a change is not significant. (interpret)
33. [Core] Use a confidence interval to determine if the mean of a new sample places the new data within the confidence interval or is statistically significantly different. (interpret)
34. [Peri] Infer from a p-value the largest confidence interval for which a change is not significant. (interpret)

35. Given two variable data and the use of spreadsheet software on a computer

Linear Regressions
36. [Core] Identify the sign of a least squares line: positive, negative, or zero. (Define)
37. [Core] Calculate the slope of the least squares line. (calculate)
38. [Core] Calculate the intercept of the least squares line. (calculate)
39. [Core] Solve for a y value given an x value and the slope and intercept of a least squares line. (solve)
40. [Core] Solve for a x value given an y value and the slope and intercept of a least squares line. (solve)
41. [Core] Calculate the correlation coefficient r. (calculate)
42. [Core] Use a correlation coefficient r to render a judgment as to whether a correlation is perfect, high, moderate, low, or none. (interpret)
43. [Core] Calculate the coefficient of determination r². (calculate)

### Instructor Intentions

• Use of Microsoft Excel and Microsoft Excel functions throughout the course as opposed to using dedicated statistics software package. Excel and other spreadsheets will be the desktop software most widely available to MS 150 students both while taking the course and, more importantly, in the workplace post-graduation.
• Use of real-world data, examples, and problems to the extent appropriate and possible.

### Assessment

Assessment will be via quizzes, tests, midterm examinations and a final examination. All core outcomes will appear on the final examination.

### Notes

[Core] outcomes are tested on the cumulative final examination and preceding quizzes, tests, and midterm examinations. Students must successfully achieve core outcomes in order to pass the class.

[Peri] outcomes are tested during the course and may appear on the final. Their achievement is used to distinguish levels of skill above a minimal pass.

In this second format the mapping is achieved by the reference in parentheses at the end of each outcome. This format makes it easier to see the flow and run of the course. The strictly mapped outline requires a good deal of decoding and rearranging before an instructor would know what to teach. The topical format says "start here" and "end here."

The topical format can also be used, at the instructor's option, chronologically.

In the original outline, included at the end of this document, the outline included a topic outline section under roman numeral II. One might argue that the strictly mapped format could have this added in order to clarify the scope and sequence of the course. I would argue strenuously against this option. This would defeat the underlying intent of the course outcomes and be horribly redundant.

The course outcomes are intended to be a complete list of the skills a student must master to pass a course. The topic outline would suggest that the topic outline has something to do with what will be taught, but that is the fundamental reason of existence of the specific student learning outcomes.

In fact, the topic outline will simply have to repeat each and every course outcome skill or it will be less complete than the contents in the course outcomes. Which leads to my second objection: done properly the topic outline becomes completely redundant.

## Original and currently approved outline

1. Course Objectives
1. General
1. Six main topics data, descriptive statistics, basic probability, probability distributions, confidence intervals, and hypothesis testing will be covered.
2. A conceptual understanding of concepts, as well as the ability to apply them toward solving statistical problems with the aid of MS Excel
3. The underlining theorems: The Law of Large Numbers and The Central Limit Theorem, will be presented from an experimental as well as a conceptual approach.
2. Specific
Note: all specific objectives are set with the following two behavioral objectives: the student will demonstrate a proficiency level of at least 70% in
1) computer assisted homework assignments emphasizing applications and a synthesis of various concepts given within one week following the presentation of material, and during
2) the quizzes, tests, mid-term and final exam
1. the student will be able to classify data as qualitative or quantitative, and cite examples of each
2. the student will be able to select appropriate class intervals and create a frequency distribution for a data set
3. the student will be able to use MS Excel to create a histogram, a cumulative frequency polygon, and percent pie charts for a data set, and will be able to modify these charts
4. the student will be able to find information from a chart, and determine if a chart is misleading
5. the student will understand the difference between a population and a sample, and between a parameter and a statistic
6. the student will understand the various measures of central tendency, including the mean, median, and mode, and be able to select the most useful for a given data set
7. the student will be able to calculate the mean, weighted mean, median, and mode of a data, both by hand and by using MS Excel
8. the student will understand the concept behind standard deviation, and how the formula works, as well as be able to calculate the standard deviation for a data set by hand and using MS Excel
9. the student will be familiar with other measures such as skew and kurtosis, and know how to find them using MS Excel
10. the student will be able to use the definition of simple probability to find the probability of various events
11. the student will understand the reasoning behind the Law of Large Numbers, and know how it is applied to situation such as a casino
12. the student will be able to use MS Excel to simulate simple events such as flipping a coin or rolling a die, and will be able to verify the Law of Large Numbers
13. the student will be able to apply the concepts of permutations and combination towards solving problems that involve counting
14. the student will be able to determine if events are mutually exclusive, and apply the appropriate addition rule
15. the student will be able to determine if two events are independent, both conceptually and by using the multiplication rule
16. the student will be able to find marginal and conditional probabilities, and understand the connection with independence
17. the student will understand the properties that determine a probability distribution, it's graph and function, and its mean and standard deviation
18. the student will understand the properties that determine a Binomial distribution, and will be able to draw its graph and solve problems involving Binomial distributions using MS Excel
19. the student will understand the difference between a discrete and a continuous distribution, and the concept of a continuity correction
20. the student will be familiar with the Normal distribution as determined by its mean and standard deviation, and be able to apply it to problems using MS Excel
21. the student will understand the concepts behind a sampling distribution, and how the Central Limit Theorem works
22. the student will understand the relationship between a point estimate and a confidence interval
23. the student will be able to calculate confidence intervals for a population proportion
24. the student will be able to calculate confidence intervals based on small samples using MS Excel
25. the student will be able to use a confidence interval as a one- sample hypothesis test
26. the student will understand the concepts involved in hypothesis testing, including types of error, and the relationship between hypothesis tests and confidence intervals
27. the student will be able to use MS Excel to conduct one-sample Z tests both with and without raw data.
28. the student will be able to conduct paired t-test using MS Excel
29. the student will be able to test equality of two sample variances using an F-test on MS Excel
30. the student will be able to chose the appropriate two sample t-test, and conduct it using MS Excel
31. the student will be able to conduct a two-sample Z test, both for means and for population proportions
32. the student, working in a small group, will be able to design, conduct, and analyze a simple statistical research project
2. Course Contents
1. Data, Types of data: Qualitative versus Quantitative
1. Frequency Distributions: Standard, Cumulative, and Percent Histograms
2. Cumulative Frequency Polygons
3. Percent Pie Charts
2. Descriptive Statistics
1. Population versus Sample/ Parameter versus Statistic
2. Measures of Central Tendency: Mean, Median, Mode
3. Measures of Variation: Standard Deviation, Percentiles
4. Other Measures: Skew and Kurtosis
3. Basic Probability
1. Simple Probability and the Law of Large Numbers
2. Counting: Permutations and Combinations
3. Basic Rules: Complements
4. Sample Space
6. Basic Rules: Multiplication and Independent Events
7. Conditional Probability
4. Probability Distributions
1. Basic Properties
2. Mean and Standard Deviation of a Probability Distribution
3. Binomial Distribution
4. The Normal Distribution
5. Sampling Distributions and the Central Limit Theorem
5. Confidence Intervals
1. Point Estimates versus Confidence Intervals
2. Confidence Intervals for Population Proportions
3. Confidence Intervals for small sample size / t-Distributions
4. Using Confidence Intervals as a One-sample Test
6. Hypothesis Testing
1. Basic concepts/ Types of error
2. One sample Z test for means, with and without raw data
3. Paired t test for means
4. F test for equal variance
5. 2 sample t tests for means
6. 2 sample z-tests for means
7. Z-test for comparison of two proportions
3. Textbook "Understanding Basic Statistics", Brase and Brase, Houghton Mifflin, 1997
4. Required course materials: Scientific calculator
5. Reference materials
1. Microsoft Excel spreadsheet mathematical software by Microsoft.
2. "Data Analysis with Microsoft Excel", Berk and Carey, Duxbury Press, 1998
3. "Statistics: A First Course", 6th ed. by Freund and Simon, Prentice Hall, Inc. 1995 (ISBN 0-13-083024-0),
4. "Elementary Statistics." 6th ed. by Johnson, PVVS-KENT Pub., 1992 (ISBN 0-534-92980-X)
6. Instructional costs: None anticipated at this time
7. Methods of Instruction: The course will be taught by lecture, class discussion, and the use of Microsoft Excel for problem solving and computer simulations. Thus, this course will be taught in the Math/Science computer classroom. Also, students will be encouraged to utilize the computer labs outside of class for homework assignments.
8. Evaluation: Homework, tests, quizzes, a midterm, and a final exam will be given. A standard 90%=A, 80%=B, 70%=c, 60%=D 50%=F grading scale is recommended. In the last month of the course, the students will work in groups of 1 to 3 on a project involving collecting and analyzing data from their own research design.
9. Credit by examination: None
10. Attendance policy: as per the current college catalog