Instructional Unit Collecting Data Statistics #316 Unit Content Objective Performance Indicator Performance Task State Standards Code:

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1 Instructional Unit Collecting Data Collecting Data The students will be - understand the difference -data collection E - population able to collect data between a population and a -classroom experiments - sample using a variety of sample and activities - parameter methods, taking into - identify the number of -problem solving and - statistic account the need for a observational units as the homework activities - biased representative sample sample size -applications to real life - simple random sample and eliminating bias. - determine if a sample is data - table of random digits biased - response variables - understand common - explanatory variables problems with biased samples - observational including convenience samples, voluntary responses, and non- response cases - identify the sampling frame for a sample - understand the concept of a simple random sample - use a table of random digits and a random number generator to create a simple random sample of data - understand the difference between a parameter and a statistic - recognize when a statistic is unbiased - recognize and understand the property of sampling variability

2 Instructional Unit Collecting Data - explore the relationship between precision of a sample statistic and sample size

3 Instructional Unit Collecting Data Collecting Data The students will be - understand and give -data collection G - population able to design examples that show the -classroom experiments - sample controlled experiments difference between and activities - parameter and control them with anecdotes, surveys, -problem solving and - statistic observational studies. observational studies, and homework activities - biased experiments -applications to real life - simple random sample - identify variables as data - table of random digits explanatory and response - response variables variables - explanatory variables - analyze the need for an - observational experiment to establish a cause-and-effect relationship between variables - model a well defined experiment that exerts several forms of control - explore the effects of lurking and confounding variables as unmonitored variables - identify and utilize the principles of a control group, randomization, and comparison as part of an experiment - determine when a causal relationship can be established between an explanatory and response variable - understand the need for controlling a placebo effect through blindness or double blindness as part of a controlled experiment - construct a well designed

4 Instructional Unit Collecting Data experiment utilizing blocking to separate subjects into similar groups

5 Instructional Unit Exploring Data: Comparisons and Relationships Exploring Data: Comparisons The students will be - construct a scatterplot -data collection B and Relationships able to explore the - determine the response and -classroom experiments - side-by-side stemplots relationships between explanatory nature of the and activities - statistical tendency variables by variables -problem solving and - outlier investigating the - determine the positive or homework activities - modified boxplots concept of association negative association from a -applications to real life - two-way table through the exploration scatterplot data - marginal and conditional of a scatterplot. - determine the strength of the distributions association form a scatterplot - seg - understand the concept of association's relationship to statistical tendency - utilize the capabilities of a graphing calculator to produce a scatterplot - produce a labeled scatterplot to show the categorical nature of subgroups of the data

6 Instructional Unit Exploring Data: Comparisons and Relationships Exploring Data: Comparisons The students will be - discover the range and sign -data collection B, and Relationships able to explore the of the possible values for a -classroom experiments C - side-by-side stemplots basic properties of the correlation coefficient and activities - statistical tendency correlation coefficient - understand that the -problem solving and - outlier as a numerical correlation coefficient homework activities - modified boxplots measure of the degree measurers only linear -applications to real life - two-way table of association relationships between data - marginal and conditional between two variables distributions variables. - utilize the capabilities of a - seg graphing calculator to compute the correlation coefficient of a set of data - understand what the correlation coefficient measures by examining the formula for its computation - explore the important distinction between association and causation - explore the concept of a lurking or confounding variable in an association - become proficient at estimating the correlation coefficient of a set of data by examining a scatterplot

7 Instructional Unit Exploring Data: Comparisons and Relationships Exploring Data: Comparisons The students will be - estimate a line of best fit -data collection B, and Relationships able to investigate least through visual inspection -classroom experiments C, - side-by-side stemplots squares regression as - understand why a least and activities D - statistical tendency a mathematical model squares line produces the best -problem solving and - outlier used to describe the line of fit homework activities - modified boxplots relationship between - determine the slope and -applications to real life - two-way table quantitative variables. intercept coefficient of a lest data - marginal and conditional squares line distributions - utilize the capabilities of a - seg graphing calculator to determine the least squares coefficients - utilize the least squares regression line to make predictions of values within the data range - examine the dangers involved in extrapolation from a least square regression equation - determine the fitted value and residual for a data point - explain the meaning of r-squared, the coefficient of determination - determine when a least squares model is appropriate for a set of data

8 Instructional Unit Exploring Data: Comparisons and Relationships Exploring Data: Comparisons The students will be - identify outliers in the -data collection C, and Relationships able to use residual context of regression lines -classroom experiments D - side-by-side stemplots plots as a measure of - identify influential and activities - statistical tendency appropriate linearity observations in the context of -problem solving and - outlier and transform data into regression lines homework activities - modified boxplots a linear relationship - utilize residual plots to -applications to real life - two-way table even when the data is indicate when a linear model data - marginal and conditional non-linear. dos not adequately describe distributions the relationship in the data - seg - transform one or both variables of non-linear data to make the association more linear Exploring Data: Comparisons The students will be - construct a side-by-side -data collection A, and Relationships able to apply stemplot -classroom experiments B - side-by-side stemplots previously learned - examine the nature of and activities - statistical tendency techniques to the statistical tendency through -problem solving and - outlier analysis, comparison the examination of a homework activities - modified boxplots and contrast of side-by-side stemplot -applications to real life - two-way table distributions from two - construct a set of parallel data - marginal and conditional or more groups boxplots distributions simultaneously. - using the 1.5IQR test - seg determine if a data point is an outlier - construct a modified boxplot - utilize the capabilities of a graphing calculator to produce a set of parallel boxplots and a modified boxplot

9 Instructional Unit Exploring Data: Comparisons and Relationships Exploring Data: Comparisons The students will be - classify variables as a -data collection A, and Relationships able to utilize basic response or explanatory -classroom experiments F - side-by-side stemplots techniques for variable and activities - statistical tendency comparing distributions - construct a two-way table -problem solving and - outlier of categorical and identify its dimensions homework activities - modified boxplots variables. - calculate the marginal -applications to real life - two-way table distribution of one variable of a data - marginal and conditional two-way table distributions - examine conditional - seg distributions to study possible relationships between two categorical variables - construct a segmented bar graph to represent conditional distributions - calculate the relative risk of two groups of the explanatory variable - discover and explore the phenomenon called Simpson's paradox - determine if two categorical variables are independent

10 Instructional Unit Exploring Data: Distributions Exploring Data: Distributions The students will be - determine the range of a set -data collection A - data able to calculate the of data -classroom experiments - variables common measures of - utilizing the concept of and activities - variability variability of a percentile, determine the -problem solving and - distributions distribution, investigate interquartile range by homework activities - bar graphs their properties, and determining the upper and -applications to real life - dotplots apply them to some lower quartiles data - stemplots genuine data. - determine the five number - histograms summary of a set of data - mean - utilize the five number - median summary to construct a - mode boxplot of a set of data - resistance - compute a measure of - range variability about a mean called the mean absolute deviation - compute a measure of variability about a mean called the standard deviation - interpret the spread of a set of data given the standard deviation and interquartile range - utilize the capabilities of a graphing calculator to compute the standard deviation and five number summary - discover the resistant nature of the measures of variability - discover how data is distributed in a symmetric distribution by the empirical rule

11 Instructional Unit Exploring Data: Distributions - standardize a score by calculating the z-score - analyze sets of different symmetric data through the use of z-scores - analyze how the shape of a distribution relates to the variability of the data

12 Instructional Unit Exploring Data: Distributions Exploring Data: Distributions The students will be - describe the features of a -data collection A, - data able to display and distribution of data using the -classroom experiments B - variables describe distributions. following six features: center, and activities - variability variability, shape, peaks and -problem solving and - distributions clusters, outliers, granularity homework activities - bar graphs - create a stemplot of a set of -applications to real life - dotplots data data - stemplots - create a histogram of a set - histograms of data - mean - utilize a stemplot and/or a - median histogram to describe the - mode features of a distribution of - resistance data - range - utilize the capabilities of a graphing calculator to create a stemplot - classify the shape of a distribution of data as symmetric, skewed to the left, or skewed to the right

13 Instructional Unit Exploring Data: Distributions Exploring Data: Distributions The students will be - enter data into the graphing -data collection A, - data able to begin using the calculator as a list -classroom experiments B - variables graphing calculator to - download a program to the and activities - variability explore statistics. calculator -problem solving and - distributions - utilize a program to create a homework activities - bar graphs dotplot of a set of data -applications to real life - dotplots - utilize the spreadsheet data - stemplots capabilities of a graphing - histograms calculator to display and - mean manipulate data - median - compute rates and - mode percentages using the list - resistance capabilities of a graphing - range calculator - download data from a computer to a graphing calculator - utilize the link command on a graphing calculator to share data

14 Instructional Unit Exploring Data: Distributions Exploring Data: Distributions The students will be - compute the mean of a set -data collection A - data able to calculate the of data -classroom experiments - variables common measures of - compute the median of a set and activities - variability center of a distribution, of data containing both an -problem solving and - distributions investigate their even and odd number of data homework activities - bar graphs properties, and apply - compute the mode of a set -applications to real life - dotplots them to some genuine of data data - stemplots data. - discover a rule for - histograms determining the mean of a set - mean of both even and odd amounts - median of data - mode - utilize the capabilities of a - resistance graphing calculator to - range determine the mean and median of a large set of data - analyze the relationship between the mean and median in symmetric distributions and skewed distributions - discover which measure of center display a resistant nature - recognize that a measure of center is not a complete description of a set of data

15 Instructional Unit Exploring Data: Distributions Exploring Data: Distributions The students will be - recognize data as numbers -data collection A - data able to appreciate data in context -classroom experiments - variables in context, classify - discover the variable nature and activities - variability variables, and discover of data -problem solving and - distributions the notion of a - identify the observational homework activities - bar graphs distribution. unit -applications to real life - dotplots - classify data as quantitative data - stemplots or categorical - histograms - recognize binary categorical - mean data - median - construct a bar graph - mode - construct a frequency table - resistance for data and explore the - range variability of the data - construct a dotplot to visualize the variable nature of a set of data - determine when a bar graph or dotplot is an appropriate visual display of a set of data

16 Instructional Unit Inference from Data: Comparisons and Relationships Inference from Data: The students will be - use a simulation to -data collection H, Comparisons and able to explore the approximate a p-value -classroom experiments B, Relationships comparison of two - review statistical and activities C, - tests of significance for proportions using a significance and assess the -problem solving and D comparing two proportions test of significance and likelihood of a sample result to homework activities - confidence interval for the a confidence interval. occur by chance alone -applications to real life difference in two population - use a formal test of data proportions significance to compare two - tests of signifi proportions - understand and apply the technical conditions necessary for this procedure to be valid - explore the magnitude of the difference between two proportions by creating a confidence interval - understand and apply the technical conditions necessary for the creation of a confidence interval - explore the effect of sample size on inference procedures - apply comparison of two proportions inference procedures to both experiments and observational studies - use technology to aid in the computation of the test of significance and the confidence interval

17 Instructional Unit Inference from Data: Comparisons and Relationships Inference from Data: The students will be - compare the inference -data collection H, Comparisons and able to explore the procedures for comparison of -classroom experiments B, Relationships comparison of two means to those for comparing and activities C, - tests of significance for means using a test of proportions -problem solving and D comparing two proportions significance and a - use a formal test of homework activities - confidence interval for the confidence interval. significance to compare two -applications to real life difference in two population means data proportions - understand and apply the - tests of signifi technical conditions necessary for this procedure to be valid - explore the magnitude of the difference between two means by creating a confidence interval - understand and apply the technical conditions necessary for the creation of a confidence interval - use technology to aid in the computation of the test of significance and the confidence interval - explore the relationship between sample size, means, and standard deviations in the two-sample t-test - review the importance of the randomization in designing experiments

18 Instructional Unit Inference from Data: Comparisons and Relationships Inference from Data: The students will be - understand the nature of -data collection F, Comparisons and able to apply the independence between two -classroom experiments E Relationships chi-square test for variables and activities - tests of significance for independence of two - calculate the expected -problem solving and comparing two proportions categorical variables. counts in a two-way table homework activities - confidence interval for the - use the format of a -applications to real life difference in two population chi-square test to establish the data proportions hypothesizes, test statistic, - tests of signifi and p-value - understand and apply the technical conditions necessary for this procedure to be valid - use technology to explore the chi-square test by using the matrix capabilities of a graphing calculator - explore the relationship between the square of the z test statistic for comparing two proportions to the x squared from the chi-square test.

19 Instructional Unit Inference from Data: Comparisons and Relationships Inference from Data: The students will be - apply a test of significance -data collection C, Comparisons and able to apply a test for the population correlation -classroom experiments D, Relationships procedure involving the - establish the hypothesizes, and activities H, - tests of significance for correlation coefficient. test statistic, p-value for this -problem solving and C comparing two proportions inference procedure homework activities - confidence interval for the - understand and apply the -applications to real life difference in two population technical conditions necessary data proportions for this procedure to be valid - tests of signifi - apply the inference procedures for the population slope - establish the hypothesizes, test statistic, p-value for this inference procedure - use technology to aid in the computation of the test of significance - understand and apply the technical conditions required for the validity of these inference procedures

20 Instructional Unit Inference from Data: Principles Inference from Data: The students will be - determine the standard error -data collection H, Principles able to explain the of a sample proportion -classroom experiments D, - properties of confidence purpose of a - state the definition of and activities B intervals confidence interval be statistical confidence -problem solving and - confidence intervals for a able to construct a - understand how changing homework activities proportion confidence interval for the confidence level effects -applications to real life - t-distributions estimating a population the confidence interval data - confidence intervals for a proportion. - calculate the critical value sample mean using the normal distribution - principals of a test - calculate and interpret a confidence interval for a population proportion - state and verify that the technical conditions are met for a set of data - explore the relationship between confidence level and the width of the confidence interval - identify the margin of error - calculate a confidence interval using technology - establish the relationship between sample size and confidence interval width - make a correct interpretation of a confidence interval

21 Instructional Unit Inference from Data: Principles Inference from Data: The students will be - calculate the estimated -data collection A, Principles able to use a standard deviation of a sample -classroom experiments B properties of confidence t-distribution to explore mean and activities C intervals and understand a - determine critical values -problem solving and - confidence intervals for a confidence interval for using a t-distribution homework activities proportion a population mean. - explore the family of -applications to real life - t-distributions t-distributions and their related data - confidence intervals for a degrees of freedom sample mean - calculate the confidence - principals of a test interval for a population mean - determine the degrees of freedom for the set of data - state and check the technical conditions for a confidence interval for a population mean - understand that the t-procedures are robust - examine the similarities between confidence intervals for a population mean and those for a population proportion - explore how the standard deviation effects the width of a confidence interval

22 Instructional Unit Inference from Data: Principles Inference from Data: The students will be - formalize the process of -data collection H, Principles able to perform a test statistical significance -classroom experiments C, - properties of confidence of significance and - state in both words and and activities D intervals interpret the results of symbols a null hypothesis -problem solving and - confidence intervals for a this test of significance - state in both words and homework activities proportion for a population symbols an alternative -applications to real life - t-distributions proportion. hypothesis data - confidence intervals for a - determine is a one-sided or sample mean two-sided test is appropriate - principals of a test - calculate the test statistic in context of a population proportion - determine the p-value - interpret the p-value for a given set of data - categorize the strength against a null hypothesis based on a p-value - interpret a p-value compared to a significance or alpha level - verify the technical conditions for performing a test of significance for a population proportion - use technology to perform a test of significance for a population proportion - establish a relationship between sample size and a test of significance

23 Instructional Unit Inference from Data: Principles Inference from Data: The students will be - compare the structure, -data collection H, Principles able to perform a test reasoning, and interpretation -classroom experiments C, - properties of confidence of significance and of significance tests for a and activities D intervals interpret the results of population mean to that for a -problem solving and - confidence intervals for a this test of significance population proportion homework activities proportion for a population mean. - state in both words and -applications to real life - t-distributions symbols a null hypothesis data - confidence intervals for a - state in both words and sample mean symbols an alternative - principals of a test hypothesis - understand and apply the technical conditions necessary for this procedure to be valid - construct a matched pairs experimental design to analyze the difference between two variables - explore the relationship between sample size and variation to statistical significance - determine and interpret the p-value in the context of the problem - use technology to aid in the computation of the test of significance and the confidence interval

24 Instructional Unit Inference from Data: Principles Inference from Data: The students will be - establish a duality nature -data collection B, Principles able to advance their between confidence intervals -classroom experiments C, - properties of confidence understanding of and tests of significance and activities D intervals confidence intervals - evaluate the significance of -problem solving and - confidence intervals for a and tests of a p-value versus the homework activities proportion significance through establishment of a level of -applications to real life - t-distributions the exploration of the significance data - confidence intervals for a duality nature between - determine the difference sample mean these two concepts, between practical and - principals of a test understanding the idea statistical significance of practical - define in context and significance versus determine the value of a type I statistical significance, error and understanding - define in context a type II type I and type II errors error and power. - use simulation to determine the power of a statistical test - explore the relationship between sample size and the power of a test - determine the size of a sample to achieve a desired level of accuracy and confidence - review the limitations of inference procedures including the potential bias of a sample

25 Instructional Unit Randomness in Data Randomness in Data The students will be - identify the symbolic -data collection A, - probability able to explore how representations for samples -classroom experiments E - simulations sample proportions and parameters and activities - equally likely events vary from sample to - understand that the goal of -problem solving and - the role of sample size sample in a predictable sampling is to estimate the homework activities - normal curves manner that will enable value of the parameter based -applications to real life - table of standard normal them to draw on the statistic data probabilities conclusions about the - recognize that sampling - sampling variability population proportion. variability is an important - sample component of sampling distributions - investigate a sampling distribution and evaluate the long-term pattern to the variation - formulate an understanding of the idea of being confident that the population proportion is within a certain distance of the sample proportion. - understand and utilize the central limit theorem - understand how the question of statistical significance relates to how often an observed sample result would occur by sampling variability or chance alone

26 Instructional Unit Randomness in Data Randomness in Data The students will be - explore the notion of -data collection A, - probability able to understand and sampling variability's -classroom experiments E - simulations investigate how relationship to sample means and activities - equally likely events sample means vary variation from sample to -problem solving and - the role of sample size from sample to sample. sample homework activities - normal curves - understand that the sample -applications to real life - table of standard normal mean is an unbiased estimator data probabilities of the population mean - sampling variability - explore the relationship - sample between the sampling distribution of sample means and the sample size - relate the central limit theorem to a sample mean - utilize the central limit theorem for a sample mean to explore sample data of means

27 Instructional Unit Randomness in Data Randomness in Data The students will be - explore the effect of -data collection I, - probability able to examine the population size and sample -classroom experiments D - simulations implications and size on the central limit and activities - equally likely events applications of the theorem calculations -problem solving and - the role of sample size central limit theorem - use the central limit theorem homework activities - normal curves focusing on how it lays to explore the unlikeness of an -applications to real life - table of standard normal the foundation for event from occurring data probabilities widely used - extend the central limit - sampling variability techniques of theorem to examples that - sample statistical inference. introduce the notion of statistical confidence - state the technical conditions necessary to use the central limit theorem Randomness in Data The students will be - create a simulation as an -data collection A, - probability able to use the idea of artificial representation of a -classroom experiments B - simulations probability to develop random process and activities - equally likely events the randomness - develop the concept of -problem solving and - the role of sample size required for a sample probability as the proportion of homework activities - normal curves to predict a population. times an event would occur if -applications to real life - table of standard normal the random process were data probabilities repeated over and over - sampling variability - list all possible outcomes in a - sample sample space - determine the expected value of a long-run average value achieved by a numerical random process

28 Instructional Unit Randomness in Data Randomness in Data The students will be - identify distributions that are -data collection I - probability able to utilize the symmetric, have a single peck -classroom experiments - simulations mathematical model at their center, and follow a and activities - equally likely events know as a normal bell-shaped curve as normal -problem solving and - the role of sample size distribution to calculate distributions homework activities - normal curves probabilities of interest. - understand the relationship -applications to real life - table of standard normal between a normal curve and data probabilities its mean and standard - sampling variability deviation - sample - recognize that the are under a normal curve is 1 - calculate the area under a normal curve for some interval - find areas under normal curves using a standard normal probability table and technology - explore the relationship between a normal curve to a density curve