NEW YORK CITY COLLEGE OF TECHNOLOGY

The City University of New York

DEPARTMENT: Mathematics COURSE: MAT 1272/ MA 272 TITLE: Statistics DESCRIPTION: An introduction to statistical methods and

statistical inference. Topics include descriptive statistics, random variables, distributions, sampling, estimation and inference, t-tests, chi-square tests and correlation.

TEXT: Introductory Statistics 6th edition Prem S. Mann John Wiley & Sons, Inc. CREDITS: 3 PREREQUISITES: MA1 1180/ MA180 or higher Prepared by: Prof. A. P. Taraporevala Pro. N. Benakli Fall 2008 A. Testing Guidelines: The following exams should be scheduled: 1. A one-hour exam at the end of the First Quarter. 2. A one-session exam at the end of the Second Quarter. 3. A one-hour exam at the end of the Third Quarter. 4. A one session Final Examination.

B. A scientific calculator is required

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Learning Outcomes for

MAT 1272/ MA 272 Statistics 1. Students will be able to collect, organize and graph raw data. 2. Students will be able to compute statistical parameters (mean, median, mode, average

deviation, variance, and sample standard deviation). 3. Students will be able to identify the binomial distribution and bell-shaped distributions

(Normal, t-distribution). 4. Students will be able to do simple counting arguments and apply simple probabilities to

events. 5. Students will be able to determine if the data supports a hypothesis to a given level of

significance. 6. Students will be able to find the least squares regression line.

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Mathematics Department Policy on Lateness/Absence

A student may be absent during the semester without penalty for 10% of the class instructional sessions. Therefore, If the class meets: The allowable absence is: 1 time per week 2 absences per semester 2 times per week 3 absences per semester Students who have been excessively absent and failed the course at the end of the semester will receive either

• the WU grade if they have attended the course at least once. This includes students who stop attending without officially withdrawing from the course.

• the WN grade if they have never attended the course.

In credit bearing courses, the WU and WN grades count as an F in the computation of the GPA. While WU and WN grades in non-credit developmental courses do not count in the GPA, the WU grade does count toward the limit of 2 attempts for a developmental course. The official Mathematics Department policy is that two latenesses (this includes arriving late or leaving early) is equivalent to one absence. Every withdrawal (official or unofficial) can affect a student’s financial aid status, because withdrawal from a course will change the number of credits or equated credits that are counted toward financial aid.

New York City College of Technology Policy on Academic Integrity

Students and all others who work with information, ideas, texts, images, music, inventions, and other intellectual property owe their audience and sources accuracy and honesty in using, crediting, and citing sources. As a community of intellectual and professional workers, the College recognizes its responsibility for providing instruction in information literacy and academic integrity, offering models of good practice, and responding vigilantly and appropriately to infractions of academic integrity. Accordingly, academic dishonesty is prohibited in The City University of New York and at New York City College of Technology and is punishable by penalties, including failing grades, suspension, and expulsion. The complete text of the College policy on Academic Integrity may be found in the catalog.

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MAT 1272 Statistics Text: Introductory Statistic, 6th edition , by P. Mann

Session Statistics Homework 1 1.1 What is Statistics p. 2

1.2 Types of Statistics p. 2-4 1.3 Population versus Sample p. 5-8 1.4 Basic Terms p. 8-10 1.5 Types of Variables p. 10-12

P. 4: 1.1, 1.2 P. 8: 1.4, 1.5, 1.7 P. 10: 1.9, 1.11 P. 12:1.15, 1.17

2 2.1 Raw Data p. 27 2.2 Organizing and Graphing Qualitative Data p. 27-32

P. 32: 2.1, 2.5, 2.7

3 2.3 Organizing and Graphing Quantitative Data p. 34-44 2.4 Shapes of Histograms p. 45-47

P. 47: 2.15, 2.17, 2.19, 2.23, 2.25, 2.29

4 2.5 Cumulative frequency Distributions p. 51-53 2.6 Stem-and-Leaf Displays p. 55-57

P. 54:2.35, 2.37, 2.39, 2.40 P. 57: 2.46, 2.47, 2.49, 2.53, 2.55

5 3.1 Measures of Central Tendency for Ungrouped Data p. 75-82 P. 83: 3.1, 3.5, 3.7, 3.11 – 3.21 odd, 3.23 (optional)

6 3.2 Measures of Dispersion for Ungrouped Data p. 87-91 P. 91: 3.39, 3.43 – 3.55 odd

7 3.5 Measures of Position p. 106-110 3.6 Box-and-Whisker Plot p. 111-113

P. 110: 3.87, 3.91 – 3.97 odd P. 113: 3.101 – 3.97 odd

8 First Examination

9 4.1 Experiment, Outcomes and Sample Space p. 133–137 4.2 Calculating Probability p. 138-143 4.3 Counting Rule p. 145-146 4.4 Marginal and Conditional Probabilities p. 146-149

P. 137: 4.3 - 4.13 odd P. 143: 4.19, 4.21, 4.27 – 4.33 odd P. 155: 4.45, 4.49, 4.51 P. 155: 4.53 (a), 4.55 (a), 4.57 (a)

10 4.5 Mutually Exclusive Events p. 150-151 4.6 Independent versus Dependent Events p. 151-153

P. 155: 4.47 (a), 4.53 (b), 4.55 (b), 4.57 (b) P. 155: 4.47 (b), 4.53 (c), 4.55 (c), 4.57 (c), 4.59, 4.61

11 4.7 Complementary Events p. 153-154 4.8 Intersection of Events and the Multiplication Rule p. 157-164 4.9 Union of Events and the Addition Rule p. 167-173

P. 155: 4.47 (c), 4.63, 4.65 P. 164: 4.70, 4.81 – 4.91 odd P. 173:4.105, 4.109 – 4.117 odd

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MAT 1272 Statistics Text: Introductory Statistic, 6th edition , by P. Mann

Session Statistics Homework 12 5.1 Random Variables p. 189-190

5.2 Probability Distributions of a Discrete Random Variable p. 191-195 P. 190: 5.2, 5.3 P. 196: 5.9, 5.14, 5.15, 5.16, 5.17, 5.19

13 5.3 Mean of a Discrete Random Variable p. 198-199 5.4 Standard Deviation of a Discrete Random Variable p. 199-203

P. 204: 5.25 – 5.35 odd

14 5.5 Factorials, Combinations, and Permutations p. 205-210 P. 210: 5.39 – 5.47 odd

15 5.6 The Binomial Probability Distribution p. 211-221 P. 221: 5.51, 5.53, 5.59 – 5.69 odd

16 Second Examination

17 6.1 Continuous Probability Distribution p. 248-251 6.2 The Normal Distribution p. 251-255 6.3 The Standard Normal Distribution p. 256-262 6.4 Standardizing the Normal Distribution p. 264-269

P. 263: 6.15 – 6.25 odd P. 269: 6.27 – 6.35 odd

18 6.5 Applications of the Normal Distribution p. 270-273 P. 274: 6.37 – 6.51 odd

19 6.6 Determining the of z and x Values when an Area Under the Normal Curve is Known p. 275-279

P. 279: 6.53 – 6.61 odd

20 6.7 The Normal Approximation to the Binomial Distribution p. 280-285

P. 285: 6.67 – 6.79 odd

21 7.1 Population and Sampling Distributions p. 297-299 7.2 Sampling and Nonsampling Errors p. 299-301 7.3 Mean and Standard Deviation of x p. 302-304

P. 302: 7.7 P. 305: 7.15, 7.19, 7.21

22 7.4 Shape of the Sampling Distribution of x p. 306-310 7.5 Applications of the Sampling Distribution of x p. 312-315

P. 311: 7.33 – 7.39 odd P. 316: 7.43, 7.49 – 7.57 odd

23 Third Examination

24 9.1 Hypothesis Tests: An Introduction p. 379-386 9.2 Hypothesis Tests about μ : σ Known p. 387-397

P. 386: 9.5, 9.7, 9.9 P. 398: 9.21, 9.23, 9.27, 9.35 (b) – 9.41 (b)

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MAT 1272 Statistics Text: Introductory Statistic, 6th edition , by P. Mann

Session Statistics Homework 25 9.3 Hypothesis Tests about μ : σ Unknown p. 401-408 P. 408: 9.49, 9.55, 9.61, 9.63 (a), 9.67 (b)

26 11.1 The Chi-Square Distribution p. 490-492 11.2 A Goodness-of-Fit Test p. 493-500

P. 492: 11.5, 11.7 P. 500: 11.13, 11.17 – 11.21 odd

27 11.3 Contingency Tables p. 502 11.4 A Test about Independence or Homogeneity p. 502-510

P. 511: 11.27-11.39 odd

28 13.1 Simple Linear Regression Model p. 556-558 13.2 Simple Linear Regression Analysis p. 558-567

P. 568: 13.21 –13.29 odd,

29 13.6 Linear Correlation p. 583-587 P. 587: 13.67, 13.72 – 13.79 all

30 Final Examination

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MAT 1272 Statistics Text: Introductory Statistic, 6th edition , by P. Mann

Statistics Homework 1.2 Types of Statistics p. 2-4 P. 4: 1.1, 1.2 1.3 Population versus Sample p. 5-8 P. 8: 1.4, 1.5, 1.7 1.4 Basic Terms p. 8-10 P. 10: 1.9, 1.11 1.5 Types of Variables p. 10-12 P. 12:1.15, 1.17 2.2 Organizing and Graphing Qualitative Data p. 27-32 P. 32: 2.1, 2.5, 2.7 2.4 Shapes of Histograms p. 45-47 P. 47: 2.15, 2.17, 2.19, 2.23, 2.25, 2.29 2.5 Cumulative frequency Distributions p. 51-53 P. 54: 2.35, 2.37, 2.39, 2.40 2.6 Stem-and-Leaf Displays p. 55-57 P. 57: 2.46, 2.47, 2.49, 2.53, 2.55 3.1 Measures of Central Tendency for Ungrouped Data p. 75-82 P. 83: 3.1, 3.5, 3.7, 3.11 – 3.23 odd 3.2 Measures of Dispersion for Ungrouped Data p. 87-91 P. 91: 3.39, 3.43 – 3.55 odd 3.5 Measures of Position p. 106-110 P. 110: 3.87, 3.91 – 3.97 odd 3.6 Box-and-Whisker Plot p. 111-113 P. 113: 3.101 – 3.97 odd 4.1 Experiment, Outcomes and Sample Space p. 133–137 P. 137: 4.3 - 4.13 odd 4.2 Calculating Probability p. 138-143 P. 143: 4.19, 4.21, 4.27 – 4.33 odd 4.3 Counting Rule p. 145-146 P. 155: 4.45, 4.49, 4.51 4.4 Marginal and Conditional Probabilities p. 146-149 P. 155: 4.53 (a), 4.55 (a), 4.57 (a) 4.5 Mutually Exclusive Events p. 150-151 P. 155: 4.47 (a), 4.53 (b), 4.55 (b), 4.57 (b) 4.6 Independent versus Dependent Events p. 151-153 P. 155: 4.47 (b), 4.53 (c), 4.55 (c), 4.57 (c),

4.59, 4.61 4.7 Complementary Events p. 153-154 P. 155: 4.47 (c), 4.63, 4.65 4.8 Intersection of Events and the Multiplication Rule p. 157-164 P. 164: 4.70, 4.81 – 4.91 odd 4.9 Union of Events and the Addition Rule p. 167-173 P. 173:4.105, 4.109 – 4.117 odd 5.1 Random Variables p. 189-190 P. 190: 5.2, 5.3 5.2 Probability Distributions of a Discrete Random Variable p. 191-195 P. 196: 5.9, 5.14, 5.15, 5.16, 5.17, 5.19 5.3 Mean of a Discrete Random Variable p. 198-199 5.4 Standard Deviation of a Discrete Random Variable p. 199-203

P. 204: 5.25 – 5.35 odd

5.5 Factorials, Combinations, and Permutations p. 205-210 P. 210: 5.39 – 5.47 odd 5.6 The Binomial Probability Distribution p. 211-221 P. 221: 5.51, 5.53, 5.59 – 5.69 odd

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MAT 1272 Statistics Text: Introductory Statistic, 6th edition , by P. Mann

Statistics Homework 6.3 The Standard Normal Distribution p. 256-262 P. 263: 6.15 – 6.25 odd 6.4 Standardizing the Normal Distribution p. 264-269 P. 269: 6.27 – 6.35 odd 6.5 Applications of the Normal Distribution p. 270-273 P. 274: 6.37 – 6.51 odd 6.6 Determining the of z and x Values when an Area Under the Normal Curve is Known p. 275-279

P. 279: 6.53 – 6.61 odd

6.7 The Normal Approximation to the Binomial Distribution p. 280-285 P. 285: 6.67 – 6.79 odd 7.2 Sampling and Nonsampling Errors p. 299-301 P. 302: 7.7 7.3 Mean and Standard Deviation of x p. 302-304 P. 305: 7.15, 7.19, 7.21

7.4 Shape of the Sampling Distribution of x p. 306-310 P. 311: 7.33 – 7.39 odd

7.5 Applications of the Sampling Distribution of x p. 312-315 P. 316: 7.43, 7.49 – 7.57 odd 9.1 Hypothesis Tests: An Introduction p. 379-386 P. 386: 9.5, 9.7, 9.9 9.2 Hypothesis Tests about μ : σ Known p. 387-397 P. 398: 9.21, 9.23, 9.27, 9.35 (b) – 9.41 (b) 9.3 Hypothesis Tests about μ : σ Unknown p. 401-408 P. 408: 9.49, 9.55, 9.61, 9.63 (a), 9.67 (b) 11.1 The Chi-Square Distribution p. 490-492 P. 492: 11.5, 11.7 11.2 A Goodness-of-Fit Test p. 493-500 P. 500: 11.13, 11.17 – 11.21 odd 11.4 A Test about Independence or Homogeneity p. 502-510 P. 511: 11.27-11.39 odd 13.2 Simple Linear Regression Analysis p. 558-567 P. 568: 13.21 –13.29 odd, 13.6 Linear Correlation p. 583-587 P. 587: 13.67, 13.72 – 13.79 all