Study Guide for Exam 1

This will be a closed-book exam. You will need a calculator. A calculator that performs arithmetic operations, reciprocals, square roots, powers and logarithms (base 10) is sufficient. Graphing calculators are permitted.

To do well on the exam, you should be able to do the following:

Chapter 1

Section 1.1: Overview

  1. Define statistics (the discipline) using action verbs.
  2. Define data.
  3. Distinguish between a population and a sample from a population.

Section 1.2: Types of Data

  1. Distinguish between a parameter and a statistic.
  2. Specify the types of data (quantitative/qualitative) and the levels of data (nominal/ordinal/interval/ratio), and identify the type and level given an example measurement.

Section 1.3: Design of Experiments (or Where Do Data Come From?)

  1. Distinguish between an observational study and an experimental study, and identify which category a study falls into given its description.
  2. Describe how an unobserved mechanism can cause confounding between two observed outcomes.

Chapter 2

Section 2.1: Overview

  1. Distinguish between descriptive and inferential statistics.

Section 2.2: Frequency Distributions

  1. Construct a frequency distribution given a (small) data set.

Section 2.3: Visualizing Data

  1. Construct a rug plot given a (small) data set. Note: rug plots are not covered in the text. See here for a reminder about rug plots.
  2. Construct a dot plot by hand given a (small) data set.
  3. Construct a frequency histogram by hand given a (small) data set.
  4. Use frequency distributions, rug plots, dot plots, and frequency histograms to compare data from two or more groups.
  5. Construct dot plots and histograms using Minitab.

Section 2.4: Measures of Center

  1. Given a frequency histogram for a data set, eyeball the mean.
  2. Compute the mean of a (small) data set.
  3. Given a frequency histogram for a data set, eyeball the median.
  4. Compute the median of a (small) data set.
  5. Explain why the median is less sensitive to outliers in a data set than the mean.

Section 2.5: Measures of Variation

  1. Explain, in plain English, what variation means in the context of a data set.
  2. Define the range of a data set.
  3. Explain, in words, how to compute the standard deviation from a data set.
  4. Specify the units of standard deviation, given the units of a data set.
  5. Use the range rule of thumb to make approximate conversions from ranges to standard deviations and vice versa.
  6. Use the standard deviation rule of thumb to determine whether a sample value is unusual given a data set’s mean and standard deviation.
  7. Given the mean and standard deviation from a data set with a bell-shaped distribution, estimate the proportion of sample values that fall within 1, 2, and 3 standard deviations from the mean.

Section 2.7: Exploratory Data Analysis

  1. Identify the “5 number summary” that is used to construct a boxplot.
  2. Construct a boxplot given a 5 number summary of a data set.

Minitab

  1. Interpret an output from Minitab generated by Stat → Basic Statistics → Display Descriptive Statistics, and extract the sample size, mean, median, mode, standard deviation, max, min, and mid-range from the output.

Chapter 3

Section 3.2: Fundamentals (of Probability)

  1. Define event, simple event, and sample space.
  2. Explain the relative frequency definition of probability.
  3. Estimate probabilities as relative frequencies given frequency data.
  4. Determine the events from a word problem (like the examples on page 95 - 97 and the homework) and compute the probability of an event using the classical approach to probability.
  5. Specify the allowed range for a probability, and identify probabilities associated with certain, likely, unlikely, and impossible events.
  6. Convert from probabilities given as proportions to probabilities given as percentages and vice versa.
  7. Relate the probability that an event does not occur to the probability that the event does occur.

Section 3.3: Addition Rule (of Probability)

  1. Define a compound event.
  2. Explain the meaning of ‘or’ in the statement “\(A\) or \(B\) occurs,” where \(A\) and \(B\) are events. Important: It is not the common English meaning of ‘or’.
  3. State the addition rule for probabilities.
  4. Use Venn diagrams to reason about the probability of compound events.
  5. Compute the probability of compound events, given the appropriate frequencies.
  6. Define complementary events, and relate the probability of an event to the probability of its complement.

Section 3.4: Multiplication Rule (of Probability): Basics

  1. Explain the difference between sampling with replacement and sampling without replacement.
  2. Explain the interpretation of a conditional probability \(P(A \mid B)\) in terms of the number of times that \(B\) occurred and the number of times \(A\) and \(B\) occurred.
  3. Explain the interpretation of a conditional probability \(P(A \mid B)\) as the probability of \(A\) given knowledge of \(B\).
  4. Give the definition of the conditional probability \(P(A \mid B)\) in terms of \(P(A \text{ and } B)\) and \(P(B)\).
  5. Explain how to ‘factor’ \(P(A \text{ and } B)\) in terms of marginal and conditional probabilities, aka the Multiplication Rule.
  6. Define the independence of two events \(A\) and \(B\) in terms of factoring the probability \(P(A \text{ and } B)\) and in terms of the conditional probabilities \(P(A \mid B)\) and \(P(B \mid A)\).

Section 3.5: Multiplication Rule (of Probability): Beyond the Basics

  1. Define the complement of an event, and identify the complement of an event on a Venn Diagram.
  2. Compute the probability that at least one event occurs using the probability that no events occur.
  3. Compute conditional probabilities from contingency tables.
  4. Compute conditional probabilities given base rates and conditional probabilities using a natural frequencies diagram.