Download Stats in Your World

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