Review Guide for MATH200, Statistics

Summary: Even if you’ve been doing all the work and keeping up with the course, the mass of material you need to know for the final can be overwhelming. This page helps you identify what’s most important in preparing for the exam.

Ideally, you look at the end of each chapter and follow these steps:

• Read the chapter Summary.
• Review the Formulas and know how to use the very few of them that aren’t replaced by our calculator.
• Make sure you can use all the Vocabulary.
• Look at the Objectives and work enough Review Exercises until you’re sure you have mastered each objective.

Bear in mind that we skipped some parts of the book. Refer back to your Schedule and Assignments sheet.

Realistically, MATH200 is not your only course (or not your only life activity, anyway), and you want some help in identifying what’s most essential. That’s what you’ll find below. The Chapter Guides and other handouts on the class Web page can help you to.

Something might be asked on the exam that was covered in the course but isn’t in the list below, but if so it won’t count a huge number of points. If you have mastered all the concepts in this list — and that means you can solve problems that use these concepts — you should earn a high score on the final exam.

Chapter 1: Data Collection

Review is on pages 56–57. Most important concepts:

• Understand the four types of data (or variables).
• Know the differences between an observational study and an experiment, with the pros and cons of each.
• Identify sources of sampling error and nonsampling error in a study or an experiment.

Chapter 2: Graphical Summaries of Data

Review is on pages 109–110. Most important concepts:

• Understand bar charts, histograms, pie charts, tables of data, stemplots; know when to use each one.
• Make a histogram for a simple list of numbers or a grouped distribution on paper. Label axes and scales correctly.
• Understand and compute relative frequency.
• Name the shape by looking at a graph; understand relation of mean and median to graph shape.
• Recognize bad practices that make misleading graphs.

Chapter 3: Numerical Summaries of Data

Review is on pages 172–173. Most important concepts:

• Use the Empirical Rule for normally distributed data.
• Understand and be able to compute z-scores. (You need the formula to convert raw score to z-score and vice versa.)
• Help with calculations and boxplot:
  Sample Statistics on TI-83/84 and MATH200A Program part 2
• Understand measures of central tendency: mean, median, mode. Be able to compute median by hand and both mean and median on calculator for grouped or ungrouped data.
• Understand measures of dispersion: range, standard deviation, variance. Compute range by hand and the other two on calculator.
• Use a boxplot on calculator to check for outliers.
• Compute the five-number summary on calculator.

Chapter 4: Correlation & Regression

Review is on pages 215–216, but the textbook chapter was replaced by a printed handout. Most important concepts:

• Make scatter plot on calculator to decide whether to perform regression. Calculator help: Scatter Plot, Correlation, and Regression on TI-83/84 (also part of the printed handout)
• Compute linear correlation coefficient r and best-fitting line ŷ = ax+b on calculator.
• Interpret r, R², slope, and intercept.
• Use the regression line to make and interpret predictions about ŷ. Calculator help: Finding ŷ from a Regression on TI-83/84 (also part of the printed handout)
• Determine whether there’s a linear relation in the population. See Decision Points for Correlation Coefficient (also part of the printed handout).

Chapter 5: Probability (Sec 5.1–5.3 only)

Review is on pages 285–286. Most important concepts:

• Understand sample space and rules of probabilities (page 224).
• Understand empirical versus classical (theoretical) methods of computing probabilities.
• Understand the Law of Large Numbers and the Gambler’s Fallacy.
• Be able to give both interpretations, probability of one and proportion of all.
• Know what makes events disjoint, complementary, independent, or mutually exclusive.
• Compute P(A^C), probability of the complement of A.
• Compute P(A or B) when A and B are disjoint.
• Compute P(A and B) when A and B are independent.
• Recognize when using the complement makes probabilities easier to compute. One common example is at-least probabilities (page 253), but you should always be alert to this technique.

Chapter 6: Discrete Random Variables

Review is on pages 319–320. Most important concepts:

• Be able to determine whether you have a binomial probability distribution or not.
• Know rules that apply to all discrete probability distributions, and those that apply only to a binomial PD.
• Compute and interpret μ and σ for general discrete PD. Calculator help: page 303
• Understand and compute expected value of a PD.
• Compute probabilities for binomial PD for a specific number of successes or a range. Calculator help: MATH200A part 3
• Compute and interpret μ and σ for binomial PD. (You need formulas, page 312.)

Chapter 7: Normal Distribution

Review is on pages 369–370. Most important concepts:

• Understand the relation of area, probability, and proportion in any density curve.
• Sketch a normal curve and shade the region of interest.
• Know the properties of the normal distribution.
• Compute area in any region of the normal curve, and compute z score or raw score that corresponds to a boundary. Calculator help:
  Normal Calculations on TI-83/84 or TI-89
• Calculate percentiles of the normal curve.
• Draw normal probability plots on calculator to test for normality. Calculator help: MATH200A part 4

Chapter 8: Sampling Distributions

Review is on page 401. Most important concepts:

• Understand concept of a sampling distribution.
• Describe shape, center, and spread for sampling distributions of the mean or the proportion. This includes knowing the requirements for the sampling distribution to be normal, for numeric or binomial data.
• Sketch the sampling distribution when it’s normal, and compute probabilities of various samples. Calculator help:
  Normal Calculations on TI-83/84 or TI-89

Chapter 9: Estimating μ and p

Review is on pages 449–450. Most important concepts:

• Compute confidence intervals about μ and p. This includes testing the requirements for a normal sampling distribution.
• Understand the properties of Student’s t distribution. Know when to use t and when to use z (the normal distribution) in estimating μ.
• Know the requirements for inferential statistics on small or large samples, numeric or binomial data.
• Understand the relation between sample size and margin of error.
• Determine necessary sample size to keep margin of error below a desired amount. Calculator procedure: MATH200A part 5
• helpful handouts for chapters 9–12:
  Inferential Statistics: Basic Cases — this one can also be used on the exam
  Triage: Which Inferential Stats Case Should I Use?

Chapter 10: Hypothesis Tests of μ and p

Review is on pages 503–504, but the textbook chapter was replaced by a printed handout. Most important concepts:

• Perform the seven steps of HT, including the unnumbered step of checking requirements. Caution: for step 6, see
  Proper Conclusions to Your Hypothesis Tests.
• Understand the p-value approach for testing hypotheses about μ and p. (Disregard the classical approach.)
• Understand the meaning of α. Choose an appropriate α for a given test.
• Be able to describe the practical effect of a Type I or Type II error in specific situations.
• Understand the relation between a HT for ≠ and a confidence interval.
• Know the difference between statistical significance and practical significance.
• helpful handout: Top 10 Mistakes of Hypothesis Tests

Chapter 11: Inferences on Two Samples

Review is on pages 552–553. Most important concepts:

• Know the difference between independent samples (unpaired data) and dependent samples (paired data).
• Test hypotheses or compute confidence intervals for two proportions, two independent means, or matched-pairs data.
• Compute necessary sample size for two population proportions. Helpful handout:
  How Big a Sample Do I Need? case 5

Chapter 12: χ² Tests (Sec 12.1–12.2 only)

Review is on pages 606–607. Most important concepts:

• Understand expected values and be able to compute them on calculator.
• Understand the requirements for performing the tests in this chapter.
• Perform a goodness-of-fit test. Calculator procedure: MATH200A part 6
• Perform a test of independence or homogeneity. Calculator procedure: MATH200A part 7 or textbook page 586