Download North Mac High School -- Pacing Guides Title of Course: Statistics

North Mac High School -- Pacing Guides
Title of Course:
Course Textbook:
ISBN#:
Instructor:
Statistics
Introductory Statistics, 6th ed.
0-201-73516-4
C. Gillespie
Major Unit of Study:
1st Quarter (August-October)
 Classify statistical studies as either descriptive or inferential. (1.1)
 Describe simple random sampling, systematic sampling, cluster sampling, and stratified sampling.
(1.3,1.4)
o S-IC.1: Understand statistics as a process for making inferences about population parameters
based on a random sample from that population.
o S-IC.3: Recognize the purposes of and differences among sample surveys, experiments, and
observational studies; explain how randomization relates to each.
 Distinguish between discrete and continuous variables and data. (2.1)
 Appropriately group data into tables, and construct appropriate graphical displays of data.
 Create and interpret a histogram. (2.3)
o S-ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
 Create and interpret a stem & leaf diagram. (2.4)
 Identify the distribution pattern of a data set. (2.5)
 Calculate, interpret, and explain, descriptive measures for both populations and samples, such as mean,
median, mode, range, standard deviation, etc. (3.1-3.3)
o S-ID.2: Use statistics appropriate to the shape of the data distribution to compare center
(median, mean) and spread (interquartile range, standard deviation) of two or more different data
sets.
 Create and interpret boxplots, noting how the interquartile range can be used to identify outliers. (3.4)
o S-ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
o S-ID.3: Interpret differences in shape, center, and spread in the context of the data sets,
accounting for possible effects of extreme data points (outliers).
 Compute and interpret population and sample z-scores. (3.5)
2nd Quarter (October-December)
 Apply basic probability rules and concepts to determine the likelihood of occurrence for a given event.
(4.1)
o S-CP.2: Understand that two events A and B are independent if the probability of A and B
occurring together is the product of their probabilities, and use this characterization to determine
if they are independent.
o S-CP.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the same as
the probability of A, and the conditional probability of B given A is the same as the probability
of B.
 Determine whether or not events are mutually exclusive. (4.2)
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o S-CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics
(or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,”
“and,” “not”).
Apply the condition probability rule to determine the likelihood of occurrence for a given event. (4.5)
o S-IC.2: Decide if a specified model is consistent with results from a given data-generating
process, e.g., using simulation.
o S-CP.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also
belong to A, and interpret the answer in terms of the model.
o S-CP.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the
answer in terms of the model.
o S-CP.8: 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.
o S-CP.9: Use permutations and combinations to compute probabilities of compound events and
solve problems.
Determine the probability distribution of a discrete random variable. (5.1)
o S-IC.1: Understand statistics as a process for making inferences about population parameters
based on a random sample from that population.
o S-MD.1: Define a random variable for a quantity of interest by assigning a numerical value to
each event in a sample space; graph the corresponding probability distribution using the same
graphical displays as for data distributions.
Determine the probability distribution for n Bernoulli trials with a given success probability. (5.3)
o S-MD.3: Develop a probability distribution for a random variable defined for a sample space in
which theoretical probabilities can be calculated; find the expected value.
o S-MD.4: Develop a probability distribution for a random variable defined for a sample space in
which probabilities are assigned empirically; find the expected value.
Determine the probability of a normally distributed random variable takes on values in a given interval.
(ch 6)
o S-ID.4: 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.
o S-MD.2: Calculate the expected value of a random variable; interpret it as the mean of the
probability distribution.
Determine the interval values for a normally distributed variable pertaining to a given percentile. (ch 6)
Assess the normality of a variable by constructing and examining the normal probability plot of sample
data. (ch 6)
3rd Quarter (January-March)
 State the relationship between sampling error and sample size. (7.1)
o S-IC.3: Recognize the purposes of and differences among sample surveys, experiments, and
observational studies; explain how randomization relates to each.
 State and apply the Central Limit Theorem. (7.3)
 Calculate the sample mean, the standard deviation of the sample mean, and determine its distribution for
varying cases where n is small or large and the population is or is not, normally distributed. (ch 7)
o S-ID.3: Interpret differences in shape, center, and spread in the context of the data sets,
accounting for possible effects of extreme data points (outliers).
o S-ID.4: 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.
 Find and interpret a confidence interval for a population mean, mu, when sigma is known. (8.2)
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find and interpret a confidence interval for a population mean, mu, when sigma is unknown. (8.4)
Demonstrate an understanding of the relationship between the sample size, standard deviation,
confidence level, and margin of error for a confidence interval for mu, by indicating how each might
change relative to the other. (ch 8)
o S-IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a
margin of error through the use of simulation models for random sampling.
Explain the two errors and the two correct decisions, possibly reached, when conducting hypothesis
testing. (9.2)
Perform an appropriate hypothesis test for a population mean, mu, when sigma is known, and interpret
the results; be able to use both the critical value and p-value approach. (9.3)
Perform an appropriate hypothesis test for a population mean, mu, when sigma is unknown and interpret
the results. (9.6)
4th Quarter (March-May)
 Calculate and interpret a confidence interval; perform hypothesis tests and interpret the results; for the
difference between two population means, when samples are paired. (10.5)
o S-ID.5: Summarize categorical data for two categories in two-way frequency tables. Interpret
relative frequencies in the context of the data (including joint, marginal, and conditional relative
frequencies). Recognize possible associations and trends in the data.
o S-IC.5: Use data from a randomized experiment to compare two treatments; use simulations to
decide if differences between parameters are significant.
 Calculate and interpret a confidence interval; perform hypothesis tests and interpret the results for a
population standard deviation. (11.1)
 Calculate and interpret a confidence interval; perform hypothesis tests and interpret the results for a
population proportion. (12.1)
 Calculate and interpret a confidence interval; perform hypothesis tests and interpret results, for the
difference between two population proportions. (12.3)
 Perform a chi-square goodness-of-fit test for the percentage distribution of a population or the
probability distribution of a random variable and interpret the results. (13.1-2)
 Obtain and graph the regression equation to make appropriate predictions. (14.1-2)
o S-ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the
variables are related.
 a. Fit a function to the data; use functions fitted to data to solve problems in the context
of the data. Use given functions or choose a function suggested by the context.
Emphasize linear, quadratic, and exponential models.
 b. Informally assess the fit of a function by plotting and analyzing residuals.
 c. Fit a linear function for a scatter plot that suggests a linear association.
o S-ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in
the context of the data.
o S-ID.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.
o S-ID.9: Distinguish between correlation and causation.
 Determine and interpret the linear correlation coefficient, r. (14.1,14.2,14.4)
Assessments Used:
 homework: 2-3 times per week
 weekly quizzes
 chapter and quarterly tests
 pre/post tests per semester
1st Semester:
_________Pre-Test Date
_________Quarterly Test Date
_________Post Test Date
2nd Semester:
_________Pre-Test Date
_________Quarterly Test Date
_________Post Test Date