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 Math Tech IV: Data Analysis and Probability  Syllabus and Correlation to SC Standards: Probability and Statistics Math Tech IV: Data Analysis M. McCarson, Hillcrest High School, 2005 2006 Correlated to Elementary Statistics by Larson and the SC Curriculum Standards Introduction to Statistics: Activity that demonstrates the parts of data analysis: collecting, displaying, and analyzing data; probability; finding confidence levels; performing hypothesis tests. Chapter 1: Introduction to Statistics August 24 Sept. 7 (SC Standards: IA1, IA2, IC3 Define statistics; compare statistic vs. parameter; inferential vs. descriptive statistics Compare quantitative vs. qualitative data; identify data sets as to their level of measurement; Identify variables as discrete or continuous Review of definitions; quiz on sections 1.1 and 1.2 Identify the type of sample; determine how the sample represents the entire population Activities demonstrating the types of samples Activities demonstrating the importance of randomization Review of Chapter 1 Case Study 1: Real Statistics vs. Real Decisions Chapter 1 test Chapter 2: Descriptive Statistics Sept. 8 Oct. 19 SC Standards IA3, IC1-2, ID13, IIA1-3, IIC1-2 Construct and interpret frequency distributions, histograms, and ogives Construct and/or interpret stem-and-leaf plots, boxplots, Pareto charts, pie charts, and time series charts Activities for collecting data, deciding the best plot to use, displaying the data, interpreting and analyzing the data Review 2.1 and 2.2; use graphing feature of graphing calculator to construct a histogram TEST on 2.1 and 2.2 Find measures of central tendency; determine the shape of distribution and position of mean and median in each distribution; determine the effect of adding a large or small data point Find the range of a data set; find the variance and standard deviation for ungrouped data Find the range, variance, and standard deviation of a set of grouped data Interpret standard deviation using the Empirical Rule and Chebyshevs Theorem Activity finding measures of central tendency and variation for data that has been collected; Case study, pg. 86 Review of 2.3 and 2.4 TEST on 2.3 and 2.4 Find the quartiles, interquartile range, and other percentiles for a given data set; make a boxplot of data; determine if a data point is an outlier Activity demonstrating boxplots Review of 2.3 TEST on 2.3 Project on collecting data, displaying data, and analyzing data with graph and statistics of central tendency and variation. Students will present data to class as part of project. Chapter 3: Probability Oct. 20 Nov. 21 Standards: IC3, ID1, IV A-2, IV B1-2, IV D1-3, IV E1 Introductory activity regarding the concept of probability and chance Identify the sample space of a probability experiment Identify and use simple events and properties of probability Distinguish among classical, empirical, and subjective probability Find the conditional probability; use the multiplication rule for sequence of events and conditional probability Distinguish between independent and dependent events Review of 3.1 to 3.2; Quiz on 3.1 and 3.2 Determine if two events are mutually exclusive; apply the additional rule to two events Activity to demonstrate probability concepts; case study pg. 139 Review of 3.3 TEST on 3.1 to 3.3 Identify when to use and then use the Fundamental Counting Principle, a combination, and/or a permutation. Apply the Fundamental Counting Principle, combinations, and permutations to probability Activity for Fundamental Counting Principle; use calculator to find probability TEST on 3.4 Simulation activities to distinguish between classical and empirical probability Chapter 4: Discrete Probability Distributions Nov. 28 Jan. 5 Standards: IB 1, IV A3, IV B1-2, IVC1 - 2 Distinguish between discrete random variables and continuous random variables Construct a discrete probability distribution and its graph given the percents and finding the percents Determine if a distribution is a probability distribution Find the mean and expected value of a probability distribution Activity to demonstrate the mean/expected value of a probability distribution Review of probability distribution TEST on 4.1 Determine if a distribution is a binomial distribution Calculate binomial probabilities using the binomial formula, tables, and/or technology Construct a graph of a binomial distribution; activity for finding a binomial distribution Review of 4.2 TEST on 4.2 Expected Value Project Students work in groups to make a game of chance that demonstrates probability distributions and expected values. Jan. 6 Jan. 13 Semester Exam Review and Exams Chapter 5: Normal Probability Distributions - Jan. 18 Feb. 10 SC Standards: I D3, III A 2, III B - 2 Interpret graphs of normal distributions including symmetry and area Use the Empirical Rule and Chebyshevs Theorem to estimate the area under a curve Find areas under the standard normal curve Review of 5.1 and 5.2 Quiz on 5.1 and 5.2 Find the probabilities for normal distributions Review of 5.3 Quiz on 5.3 Find a z-score given the area under the normal curve Transform a z-score to an x-value; find a specific data value of a normal distribution Review on 5.4 TEST on 5.4 Define and recognize a sampling distribution; find the mean and standard deviation of the sampling distribution Activity for Central Limit Theorem Find the probability of a sampling distribution using the Central Limit Theorem TEST on 5.5 Chapter 6: Confidence Intervals Feb. 13 March 3 SC Standards: III D1 Introductory Activity Construct and interpret confidence intervals for the population mean Estimate the required sample size for given level and standard deviation Review of 6.1 Quiz on 6.1 Activity for introduction to one sample proportion confidence intervals Construct a confidence interval for a population proportion Review of 6.3 Quiz on 6.3 Application of confidence intervals to control charts in industry and manufacturing Review of Chapter 6 Chapter 6 Test Chapter 7: Hypothesis Testing with One Sample March 6 March 23 SC Standards: III A1-2, III D2 Introduction to hypothesis testing activity State the null and alternative hypothesis Identify Type I and Type II errors; determine if the test is one-tailed or two-tailed test Find a P-value and make and interpret a decision based on the results; write a claim in terms of the hypothesis. Review of 7.1 and 7.2 TEST on section 7.1 and 7.2 Introduction to using proportions in hypothesis testing Use the z-test to test a population proportion p Review of section 7.4 TEST on section 7.4 Project with hypothesis test. Students will use hypothesized mean or proportion, collect data, test hypothesis, and present results. Chapter 8: Hypothesis Testing with Two Samples (Using Technology) March 24 March 31 Perform a two-sample z-test for the difference between two means or two proportions Set up null and alternative hypothesis for the test Determine the p-value Make a conclusion based on p-value and level of significance Review of 8.1 and 8.4 Test on 8.1 and 8.4 Chapter 10: Chi-Square Tests April 3 April 26 SC Standards: IIIA1 - 2 Introductory activity to goodness of fit Use a chi-square distribution to test whether a frequency distribution fits a claimed distribution Quiz on 10.1 Use a contingency table to find expected frequencies Use a chi-square distribution to test whether two variables are independent Collect data to present in a contingency table and perform a chi-square test of independence Quiz on 10.2 Review Chapter 10 Test on Chapter 10 Chapter 9: Correlation and Regression April 27 May 24 SC Standards: IB2, ID5, IIB 1-4, IID 1-2 Review of Slope: Find the slope given two points, a line. Find the equation of a line given two points or a line. Quiz on Slope Introductory activity for regression and correlation Identify independent and dependent variables and the types of correlations Find and estimate a correlation coefficient from a description or graph Find the equation of a regression line Activity to collect data for scatter plot and regression line. Predict values using the regression line; interpret the slope of the regression line. Review of 9.1 and 9.2 Chapter 9 Test Optional Unit: Experimental Design teacher supplemented May 25 May 31 Exam Review, Exams |
