Howard Community College Math 138 – Statistics Course Objectives Written in Power Point format Michael O’Donnell

Legend (colors used) Blue : Part of the syllabus Green: Not part of the syllabus but an important statistical or applied topic that will be covered if time permits Violet: Not explicitly listed in the syllabus, but I have seen questions covering this topic on past tests, and so will be covered. Brown: Listed in the syllabus and covered in class, and may be required for homework, but normally not on tests.

Division of Mathematics, HCC Course Objectives for Chapter 2 After studying this chapter, the student will be able to: Determine the context for the data values. Identify the six W’s in any data set: Who, What, When, Where, Why, How. Identify the cases and variables in any data set. Classify a variable as categorical or quantitative. Identify units for quantitative data. Identify the population from which a sample was chosen.

Division of Mathematics, HCC Course Objectives for Chapter 3 After studying this chapter, the student will be able to: Appropriately display categorical data using a frequency table, bar chart, or pie chart. Using a contingency table, determine marginal and conditional distributions, noting any anomalies or extraordinary features revealed by the display of a variable. Recognize when events are independent. Recognize a situation that involves Simpson’s Paradox.

Division of Mathematics, HCC Course Objectives for Chapter 4 After studying this chapter, the student will be able to: Appropriately display quantitative data using a frequency distribution, histogram, relative frequency histogram, stem-and-leaf display, dotplot. Describe the general shape of a distribution in terms of shape, center and spread. Describe any anomalies or extraordinary features revealed by the display of a variable. Compute and apply the concepts of mean and median to a set of data. Compute and apply the concept of the standard deviation and IQR to a set of data. Select a suitable measure of center/spread for a variable based on information about its distribution. Create a five-number summary of a variable.

Division of Mathematics, HCC Course Objectives for Chapter 5 After studying this chapter, the student will be able to: Construct a boxplot by hand. Construct side-by-side boxplots for two or more groups. Construct side by side histograms on comparable scales to compare the distributions of two groups. Compare the distributions of two or more groups by comparing their shapes, centers, spreads, and unusual features. Use the 1.5 IQR rule to identify possible outliers. Display quantitative data over time using a timeplot.

Division of Mathematics, HCC Course Objectives for Chapter 6 After studying this chapter, the student will be able to: Compare values from two different distributions using their z-scores. Use Normal models (when appropriate) and the 68-95-99.7 Rule to estimate the percentage of observations falling within one, two, or three standard deviations of the mean. Determine the percentages of observations that satisfy certain conditions by using the Normal model and determine “extraordinary” values, and the reverse. Determine whether a variable satisfies the Nearly Normal condition by making a normal probability plot or histogram. Note: It is essential that this chapter be mastered. Almost everything in Unit 3 depends on it.

Division of Mathematics, HCC Course Objectives for Chapter 7 After studying this chapter, the student will be able to: 24. Use a scatterplot to determine if a linear correlation is suggested between two variables and describe the correlation with regard to direction, form and scatter. 25. Compute the correlation of two variables and use it as part of the description of a scatterplot. 26. Identify and describe points that deviate from the overall pattern.

Division of Mathematics, HCC Course Objectives for Chapter 8 After studying this chapter, the student will be able to: Compute a linear equation that models the relationship between two variables. Determine whether the slope of a regression line makes sense and interpret the slope in the context of the problem. Know how to use a plot of residuals against predicted values to check the straight enough condition or look for outliers. Find the residual for a given x. Use regression to predict a value of y for a given x.

Division of Mathematics, HCC Course Objectives for Chapter 11 After studying this chapter, the student will be able to: Accurately model a situation through simulation. Discuss the results of a simulation study and draw conclusions about the questions being investigated.

Division of Mathematics, HCC Course Objectives for Chapter 12 After studying this chapter, the student will be able to: Classify samples, populations, parameters and statistics. Identify and explain the different sampling techniques: census, simple random samples, stratified, cluster, systematic and convenience. Recognize different types of bias. Recognize other limitations of sampling.

Division of Mathematics, HCC Course Objectives for Chapter 13 After studying this chapter, the student will be able to: Recognize the difference between an experiment and an observational study. Identify observational studies as retrospective (case-control) or prospective (longitudinal, cohort) or cross-sectional. Explain what a lurking variable is. Explain confounding. Explain the stages of a clinical trial.

Division of Mathematics, HCC Course Objectives for Chapter 14 After studying this chapter, the student will be able to: Apply the Law of Large Numbers. Recognize when events are disjoint and when events are independent. State the basic definitions and apply the rules of probability for disjoint and independent events.

Division of Mathematics, HCC Course Objectives for Chapter 15 After studying this chapter, the student will be able to: State the definition of sample space, event and P(A). Apply the General Addition and General Multiplication rules. Compute conditional probabilities and use the rule to test for independence. Know how to make and use a tree diagram to understand conditional probabilities and reverse conditioning.

Division of Mathematics, HCC Course Objectives for Chapter 16 After studying this chapter, the student will be able to: Define random variable and recognize random variables. Find the probability model for a discrete random variable. Find and interpret in context the mean (expected value) and the standard deviation of a random variable.

Division of Mathematics, HCC Course Objectives for Chapter 17 After studying this chapter, the student will be able to: Tell if a situation involves Bernoulli trials. Know the appropriate conditions for using a Binomial or Normal model. Find the mean and standard deviation of a Binomial model. Calculate binomial probabilities, perhaps with a Normal model. Find the mean and standard deviation of a Geometric model. Calculate and interpret Geometric probabilities. Calculate and interpret Poisson probabilities.

Division of Mathematics, HCC Course Objectives for Chapter 18 After studying this chapter, the student will be able to: State and apply the conditions and uses of the Central Limit Theorem. Determine the mean and standard deviation (standard error) for a sampling distribution of proportions or means. Apply the sampling distribution of a proportion or a mean to application problems.

Division of Mathematics, HCC Course Objectives for Chapter 19 After studying this chapter, the student will be able to: Construct a confidence interval for a proportion and interpret the constructed confidence interval in the context of the problem, checking the necessary assumptions and conditions. Determine the sample size necessary to produce a certain margin of error. Fully interpret the Gallup poll reported on at the beginning of this presentation!

Division of Mathematics, HCC Course Objectives for Chapter 20 After studying this chapter, the student will be able to: Perform a one-proportion z-test, to include: writing appropriate hypotheses, checking the necessary assumptions and conditions, drawing an appropriate diagram, computing the P-value, making a decision, and interpreting the results in the context of the problem.

Division of Mathematics, HCC Course Objectives for Chapter 21 After studying this chapter, the student will be able to: Explain Type I and Type II errors in the context of the problem. Define power and recognize its importance in statistical inference. 

Division of Mathematics, HCC Course Objectives for Chapter 22 After studying this chapter, the student will be able to: Find a confidence interval for the difference between two proportions. Finding the z that corresponds to the percent Computing the interval Interpreting the interval in context. Perform a two-proportion z-test, to include: writing appropriate hypotheses, checking the necessary assumptions and conditions, drawing an appropriate diagram, computing the P-value, making a decision, and interpreting the results in the context of the problem.

Division of Mathematics, HCC Course Objectives for Chapter 23 After studying this chapter, the student will be able to: Perform a t-test for the population mean, to include: writing appropriate hypotheses, checking the necessary assumptions and conditions, drawing an appropriate diagram, computing the P-value, making a decision, and Interpreting the results in the context of the problem. Find a t-based confidence interval for the population mean, to include: Finding the t that corresponds to the percent Computing the interval Interpreting the interval in context.

Division of Mathematics, HCC Course Objectives for Chapter 24 After studying this chapter, the student will be able to: Perform a two-sample t-test for two population means, to include: writing appropriate hypotheses, checking the necessary assumptions and conditions, drawing an appropriate diagram, computing the P-value, making a decision, and Interpreting the results in the context of the problem. Find a t-based confidence interval for the difference between two population means, to include: Finding the t that corresponds to the percent Computing the interval Interpreting the interval in context.

Division of Mathematics, HCC Course Objectives for Chapter 25 After studying this chapter, the student will be able to: Find a paired confidence interval, to include: Finding the t that corresponds to the percent Computing the interval Interpreting the interval in context. Perform a paired t-test, to include: writing appropriate hypotheses, checking the necessary assumptions and conditions, drawing an appropriate diagram, computing the P-value, making a decision, and interpreting the results in the context of the problem.

Division of Mathematics, HCC Course Objectives for Chapter 26 After studying this chapter, the student will be able to: Perform chi-square tests for goodness-of-fit, homogeneity, and independence, to include: writing appropriate hypotheses, checking the necessary assumptions and conditions, drawing an appropriate diagram, computing the P-value, making a decision, and interpreting the results in the context of the problem.