Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
A Correlation of Stats in Your World Bock, Mariano, ©2012 To the Tennessee Mathematics Standards Statistics Bid Category 13-110-10 A Correlation of Stats in Your World, Bock, Mariano, ©2012 to the Tennessee Mathematics Standards - Statistics Tennessee State Mathematics Standards Statistics Stats in Your World ©2012 Exploring Data Interpreting Categorical and Quantitative Data (S-ID) Understand, represent, and use univariate data. 1. Understand the term 'variable' and SE/TE: Chapter 2: 9-10, 12-16, differentiate between the data types: Chapter 3: 20-38, Chapter 4: 45-71 measurement, categorical, univariate and bivariate. 2. Understand histograms, parallel box plots, and scatterplots, and use them to display and compare data. SE/TE: Chapter 4: 46-48, 52-55, 57, 60-64, 67-69, 71, Chapter 5: 84, 86-101 3. Summarize distributions of univariate data. SE/TE: Chapter 4: 46, 51-71, Chapter 5: 84-101, Chapter 6: 120-121 4. Compute basic statistics and understand the distinction between a statistic and a parameter. SE/TE: Chapter 5: 84-85, 87-88, 90, Chapter 6: 119, Chapter 10: 222, Chapter 11: 249 5. For univariate measurement data, be able to display the distribution, describe its shape; select and calculate summary statistics. SE/TE: Chapter 4: 51-71, Chapter 5: 84-101, Chapter 6: 120-121 6. Recognize how linear transformations of univariate data affect shape, center, and spread. SE/TE: Chapter 5: 95-100, 102-103, 107, 110, 112, Chapter 6: 116-119 7. Analyze the effect of changing units on summary measures. SE/TE: Chapter 5: 96, 98-99, 107, 110, 112, Chapter 6: 118-119 8. Construct and analyze frequency tables and bar charts. SE/TE: Chapter 3: 22-25, 30-31, 33, 35-36, Chapter 4: 62 9. Describe individual performances in terms of percentiles, z-scores, and t-scores SE/TE: Chapter 6: 116-119, 121, 123-127 Understand, represent, and use bivariate data. 10. Explore categorical data. SE/TE: Chapter 2: 9-10, 12-16, Chapter 3: 20-38, Chapter 21: 495-496, 498-509 11. Display and discuss bivariate data where at least one variable is categorical. SE = Student Edition, TE = Teacher’s Edition SE/TE: Chapter 7: 139, 141, 158, 160, Chapter 8: 178, Chapter 9: 206 1 A Correlation of Stats in Your World, Bock, Mariano, ©2012 to the Tennessee Mathematics Standards - Statistics Tennessee State Mathematics Standards Statistics Stats in Your World ©2012 12. For bivariate measurement data, be able to display a scatterplot and describe its shape; use technological tools to determine regression equations and correlation coefficients. SE/TE: Chapter 5: 94-95, Chapter 7: 139-155, 156-162, Chapter 8: 165-179, 184-190, Chapter 9: 192, 194-208, 209-215 13. Identify trends in bivariate data; find functions that model the data and that transform the data so that they can be modeled. SE/TE: Chapter 7: 139-149, 152-153, Chapter 8: 164-183, Chapter 9: 192-206 Probability Conditional Probability and the Rules of Probability (S-CP) Understand and apply basic concepts of probability. 1. Describe events as subsets of a sample SE/TE: Chapter 13: 288-290, 294-303, space (the set of outcomes) using Chapter 14: 306-318, Chapter 15: 320characteristics(or categories) of the 341, Chapter 16: 344, 346-347 outcomes, or as unions, intersections, or complements of other events(“or,” “and,” “not”). 2. Use permutations and combinations to compute probabilities of compound events and solve problems. SE/TE: Chapter 13: 291-297, 301-303, Chapter 16: 351-354, 362, 364-367 3. Demonstrate an understanding of the Law of Large Numbers (Strong and Weak). SE/TE: Chapter 13: 286-287, 297-299, Chapter 14: 306, 313 Use the rules of probability to compute probabilities of compound events in a uniform probability model. 4. Demonstrate an understanding of the SE/TE: Chapter 14: 307-318, Chapter 15: addition rule, the multiplication rule, 320-329, 330-334, 336-341, Chapter 16: conditional probability, and independence. 352-353, 362, 366, Chapter 17: 372, 386, Chapter 21: 495-496 5. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. SE = Student Edition, TE = Teacher’s Edition SE/TE: Chapter 14: 309-318, Chapter 15: 330-334, 336-341 2 A Correlation of Stats in Your World, Bock, Mariano, ©2012 to the Tennessee Mathematics Standards - Statistics Tennessee State Mathematics Standards Statistics Stats in Your World ©2012 Probability Distributions Using Probability to Make Decisions (S-MD) Understand and use discrete probability distributions. 1. Define a random variable for a quantity of SE/TE: Chapter 16: 343-367, Chapter 17: interest by assigning a numerical value to 371-395, Chapter 18: 397-418, Chapter 19: 420-456, Chapter 20: 458each event in a sample space; graph the 492, Chapter 21: 494-516 corresponding probability distribution using the same graphical displays as for data distributions. 2. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. SE/TE: Chapter 16: 343-346, 362-367 3. Design a simulation of random behavior and probability distributions. SE/TE: Chapter 12: 266-272, 274-277, 279-281 4. Analyze discrete random variables and their probability distributions, including binomial and geometric. SE/TE: Chapter 16: 343-348, 350-356, 358-361 5. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. SE/TE: Chapter 16: 344, 346-353, 355, 357-358, 360-367, Chapter 17: 374, 389, 391-392, Chapter 21: 495, 508-509, 511, 513, 515 6. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? SE/TE: Chapter 16: 343-346, 353-357, 362-367, Chapter 17: 371, 375-380, 383384, 386-387, 389-395, Chapter 18: 399404, 409-418, Chapter 19: 422-424, 428456, Chapter 20: 465-492, Chapter 21: 494, 496-516 7. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. SE/TE: Chapter 13: 288-289, 291-295, 300-302, Chapter 14: 313, 317, Chapter 16: 343-347, 363-367 SE = Student Edition, TE = Teacher’s Edition 3 A Correlation of Stats in Your World, Bock, Mariano, ©2012 to the Tennessee Mathematics Standards - Statistics Tennessee State Mathematics Standards Statistics Stats in Your World ©2012 a. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. SE/TE: Chapter 13: 288-289, 291-295, 300-302, Chapter 14: 313, 317, Chapter 16: 344, 346, 364-367 b. Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a lowdeductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. SE/TE: Chapter 13: 291-295, 301-302, Chapter 14: 313, 317, Chapter 16: 343347, 363-367 8. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). SE/TE: Chapter 13: 291, 293-295, 300302, Chapter 14: 313, 317, Chapter 16: 343-345, 349-351, 357-361, 363-367 9. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). SE/TE: Chapter 13: 293-295, 301-303, Chapter 14: 317-318, Chapter 15: 327, Chapter 16: 364-367, Chapter 18: 402403, 414-418, Chapter 19: 443-445, 450456, Chapter 20: 468-469, 472-478, 480, 485-490 Understand the normal probability distribution. 10. Calculate the mean (expected value) and SE/TE: Chapter 16: 343-348, 356-357, standard deviation of both a random variable 359, 362-367 and a linear transformation of a random variable. 11. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. SE/TE: Chapter 4: 61-65, 69-70, 73-81, Chapter 6: 115-136, Chapter 16: 355-361, 365-367, Chapter 17: 371-372, 374-377, 379-380, 382-383, 389-395, Chapter 18: 401, 403-409, Chapter 19: 420-424, 426435, 449-451, 453-456 Sampling and Experimentation Making Inferences and Justifying Conclusions (S-IC) Know the characteristics of well-designed studies. 1. Understand the differences among various SE/TE: Chapter 11: 242-253, 257-259 kinds of studies and which types of inferences can be legitimately drawn from each. 2. Compare census, sample survey, experiment, and observational study. SE = Student Edition, TE = Teacher’s Edition SE/TE: Chapter 10: 219-233, 236-240, Chapter 11: 242-254, 256-264, Chapter 17: 374, 382-386, Chapter 18: 398-408, 411-412, Chapter 20: 464-482 4 A Correlation of Stats in Your World, Bock, Mariano, ©2012 to the Tennessee Mathematics Standards - Statistics Tennessee State Mathematics Standards Statistics Stats in Your World ©2012 3. Describe the role of randomization in surveys and experiments. SE/TE: Chapter 10: 220, 223-228, 234, Chapter 11: 243-248, 251-252, 254, 256, Chapter 12: 266-278 4. Demonstrate an understanding of bias in sampling. SE/TE: Chapter 10: 218, 219-220, 229233, 237-239 5. Describe the sampling distribution of a statistic and define the standard error of a statistic. SE/TE: Chapter 17: 371-374, 377, 380, 383-385, Chapter 18: 397, 401, 404, 407409, Chapter 19: 420-424, 426, 429, 432434, Chapter 20: 459-481, Chapter 21: 497-499 6. Demonstrate an understanding of the Central Limit Theorem. SE/TE: Chapter 19: 420-426, 444-447 Design and conduct a statistical experiment to study a problem, then interpret and communicate the outcomes. 7. Select a method to collect data and plan SE/TE: Chapter 10: 219-221, 223-233, and conduct surveys and experiments. Chapter 11: 242-257 8. Compare and use sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. SE/TE: Chapter 10: 218, 219-233, 234236, 237-240, Chapter 11: 249 9. Test hypotheses using appropriate statistics. SE/TE: Chapter 18: 397-405, 407-411, 413, Chapter 19: 431-440, 442, Chapter 20: 464-468, 475-481, Chapter 21: 497509 10. Analyze results and make conclusions from observational studies, experiments, and surveys. SE/TE: Chapter 10: 220, 223-228, 233, Chapter 11: 243-248, 251-253, 255, 256257 11. Evaluate reports based on data. SE/TE: Chapter 4: 59-60, 71, Chapter 5: 99, 101, Chapter 6: 129, Chapter 7: 153, Chapter 8: 168-170, Chapter 9: 206-207, Chapter 15: 321-323, Chapter 16: 357359, Chapter 17: 379-381, 386-387, Chapter 18: 411, Chapter 20: 464-466, 481-482 SE = Student Edition, TE = Teacher’s Edition 5 A Correlation of Stats in Your World, Bock, Mariano, ©2012 to the Tennessee Mathematics Standards - Statistics Tennessee State Mathematics Standards Statistics Stats in Your World ©2012 Make inferences about population parameters based on a random sample from that population. 12. Develop and evaluate inferences and SE/TE: Chapter 5: 94-95, Chapter 7: predictions that are based on data. 139-153, Chapter 8: 164-180, Chapter 9: 192-207, Chapter 17: 371-374, 377, 380, 383-385, Chapter 18: 397, 401, 404, 407-409, Chapter 19: 420-424, 426, 429, 432-434, Chapter 20: 459-481, Chapter 21: 497-499 13. Use properties of point estimators, including biased/unbiased, and variability. SE/TE: Chapter 17: 371-374, 376-377, Chapter 19: 419-424 Additional opportunities to address this standard are available, please see: SE/TE: Chapter 10: 219, 229-233 Understand and use confidence intervals. 14. Understand the meaning of confidence level, of confidence intervals, and the properties of confidence intervals. SE/TE: Chapter 17: 375-387, Chapter 18: 405, Chapter 19: 430-431, Chapter 20: 460-467, 469-480, 483 15. Construct and interpret a large sample confidence interval for a proportion and for a difference between two proportions. SE/TE: Chapter 17: 377-381, 383-385, Chapter 18: 405, Chapter 20: 460-468, 483 16. Construct the confidence interval for a mean and for a difference between two means. SE/TE: Chapter 19: 427-431, 444-447, Chapter 20: 468-480, 483 Use distributions to make inferences about a data set. 17. Apply the properties of a Chi-square SE/TE: Chapter 21: 496-501, 504-509, 510 distribution in appropriate situations in order to make inferences about a data set. 18. Apply the properties of the normal distribution in appropriate situations in order to make inferences about a data set. SE/TE: Chapter 6: 115-136, Chapter 16: 355-361, 365-367, Chapter 17: 374-377, 379-380, 382-383, Chapter 18: 400-401, 403-404, Chapter 19: 420-424 19. Interpret the t-distribution and determine the appropriate degrees of freedom. SE/TE: Chapter 19: 425-429, 431-434, 436-440, 442, 444-447 SE = Student Edition, TE = Teacher’s Edition 6