Statistics 250 Honors

Readiness Assessment Tests (RATs)

There will be in-class Readiness Assessment Tests (RATs) during most Monday classes. These tests are closed-book. Below is a list of the readings that will be covered (the list is updated on the Friday before a RAT).

You can look at the sample RAT (with answers) that we took in class on Monday, Jan. 13.

Date of RATTopics covered What to focus on
Mon., Jan. 20 Section 2.7 (pp. 40-45) in textbook
  • Know what is meant by a bell-shaped curve and know that a normal curve is a special case
  • Understand the concept of standard deviation
  • Know how to calculate the standard deviation by hand for a simple example
  • Know the empirical rule and how to apply it to simple examples like Example 2.11
  • Know how to compute a standardized score or z-score from an observed value if you also know the mean and standard deviation
Mon., Jan. 27 Section 9.2 (pp. 261-265) in textbook Note that a binomial experiment is a situation in which we take a random sample of size n from a population consisting of yes's and no's. It is assumed that the proportion of yes's in the population equals p. An example would be flipping a coin n times (in which case "heads" might be considered "yes") or asking a random sample of n people whether they are in favor of some law.
  • Know the difference between the true (population) proportion, p, and the sample proportion, p-hat. One is a parameter, the other a statistic.
  • Know how to compute p-hat from sample data.
  • Know what the normal curve approximation rule says.
  • Know the conditions that must be met for the approximation rule to apply.
  • Understand the scenarios given in the book for which the approximation rule applies.
  • Know how to compute the standard error of p-hat from sample data (the standard error of a statistic is an estimate of the standard deviation of its sampling distribution).
Mon., Feb. 3 Introduction and first two sections of Chapter 11 (pp. 313-317) in textbook
  • Know the five steps in any hypothesis test
  • Know what a null hypothesis is (box on p. 314)
  • Know what an alternative hypothesis is (box on p. 315)
  • For examples such as 11.1 and 11.2, know the difference between a one-sided hypothesis and a two-sided hypothesis test
  • Understand the "innocent until proven guilty" logic of a hypothesis test (assume the null is true, then compute whether that assumption makes the observed data very unlikely to have occurred)
Mon., Feb. 10 Section 11.6 (pp. 334-335) and all of Chapter 3 (pp. 53-74)
  • 11.6: Understand the difference between practical significance and statistical significance
  • 3.1: Know the fundamental rule for using data for inference
  • 3.1: Know the definition of simple random sample
  • 3.2: Know the difference between an observational study and a randomized experiment
  • 3.2: Know what a confounding variable is and what effect it can have
  • 3.3: Understand that cause-and-effect relationships may be established by randomized experiments but not observational studies
  • 3.3: Know the terms control group, placebo, single-blind, and double-blind
Mon., Feb. 17 Section 15.2 (pp. 468-473) and Section 12.1 (pp. 347-350)
  • 15.2: Read and understand (but don't memorize) the shortcut formula for the chi-square statistic for a 2x2 table
  • 15.2: Understand when a chi-square test on a 2x2 table is equivalent to a Z-test for a difference in two proportions
  • 15.2: Understand what Fisher's exact test is used for
  • 12.1: Know how to recognize which of the four situations on pp. 348-349 a research question falls into
  • 12.1: Know which parameters (and sample estimates) are associated with each of the four research situations
  • 12.1: Understand how paired data may be viewed as a special case of one mean
Mon., Feb. 24 Sections 4.1 through 4.3 (pp. 81-98) in textbook
  • Understand the fact regarding sample size in the last paragraph of p. 81
  • Understand the three types of bias named on p. 84
  • Know what stratified random sampling is (p. 87)
  • Know what cluster sampling is (p. 88)
  • Know what systematic sampling is (p. 89)
  • Understand the five problems listed at the top of p. 93
  • Read and understand all of the examples
Mon., Mar. 3 Chapter 13 (pp. 385-415)
  • Know the general formula for a standardized statistic near the middle of page 386
  • Know the five steps in any hypothesis test
  • Know how to formulate hypotheses correctly for each of the testing situations in Sections 13.2, 13.3, 13.4
  • Know which testing situations require Z-statistics as the standardized statistics and which situations require T-statistics instead
  • Know the necessary conditions for each test; these are the same as in Chapter 12 and may be found on pages 388, 397, and 405
  • Understand how the standard error for the difference of two proportions is different in Section 13.4 than in Section 12.6
  • Understand the relationship between two-sided tests and confidence intervals in 13.5 (don't worry about the relationship between one-sided tests and confidence intervals)
  • Know what the multiple-testing phenomenon in Section 13.6 refers to
  • Know the definition of power and know what things can affect the power of a test
Mon., Mar. 17 First Monday after spring break No RAT this week
Mon., Mar. 24 Sections 14.1 through 14.3 (pp. 425-438) in textbook You should know the assumptions about the population deviations from the regression line; in general, be well familiar with the brown box on page 431.

In addition, you should be able to do all of the following, given full or partial regression output from Minitab:

  • Find and interpret r-squared
  • Calculate y-hat for a given value of x
  • Calculate a t-statistic from the coef and SE coef
  • Locate and interpret the p-value for the slope
  • Interpret the sign of the slope (same as the sign of r)
  • Locate and interpret the standard deviation
Mon., Mar. 31 Sections 14.4 through 14.6, 16.3 (pp. 439-447 and pp. 503-507)
  • In sections 14.4 and 14.5, understand the difference between a prediction interval for y and a confidence interval for E(Y). (Do not memorize any formulas.)
  • Know all of the conditions for linear regression on pp. 443-444.
  • Know what a residual plot is and what it should look like if the regression conditions hold.
  • Know which condition a histogram or normal probability plot of the residuals would check.
  • Know that nonparametric tests like the Kruskal-Wallis test or Mood's median test may be used in place of ANOVA when the conditions for ANOVA are not satisfied.
  • Know which hypotheses are being tested by a Kruskal-Wallis test or Mood's median test.
Mon., Apr. 7 Sections 7.2 through 7.3 (pp. 176-186)
  • Understand the relative frequency interpretation of probability
  • Understand what the book means by the personal probability interpretation
  • For all of the examples in Section 7.3, understand what is meant by the sample space, a simple event, and an event.
  • For all of the examples, understand what complementary events and mutually exclusive events are. Note that complementary events are always mutually exclusive, but not necessarily the other way around. Also note that disjoint means the same thing as mutually exclusive.
  • Study examples 7.7 and 7.8 and understand what independent/dependent events are in that context
  • Understand what conditional probabilities mean in the context of example 7.8
Mon., Apr. 14 All of Chapter 1 (pp. 1-10) Read and understand each of the seven case studies along with the accompanying "morals of the stories". Make sure you can answer all of the exercises at the end of the chapter that don't ask you to use data in any way. (For instance, you can safely ignore exercises like 1.7, though I'm hoping you could do this using Minitab if you needed to!)
Mon., Apr. 21
Last RAT
of the semester!
Sections 7.4 (pp. 186-192), 7.7 (pp. 202-208), and 8.5 (pp. 233-235).
  • In Section 7.4, know all of the basic rules for finding probabilities (these are summarized on p. 193):
    • Rules 1 and 2 can be easily derived using Venn diagrams (try it!).
    • Rule 4 can also be derived using Venn diagrams if you recall that conditioning on an event means that event becomes the new sample space.
    • Rule 3 should be memorized; in fact, rule 3 is often taken to be the definition of independence.
  • Understand all examples in section 7.4
  • Know the difference between sampling with replacement and sampling without replacement
  • Know how to correctly answer questions such as the one posed by Eddy on p. 202
  • Know what sensitivity and specificity of a test refer to
  • Don't worry much about the stuff on coincidences and the gambler's fallacy in Section 7.7
  • Know what a density function for a continuous random variable is
  • Know what the density function for a uniform random variable looks like
  • Know how to find the probability that a given uniform random variable lies in a given interval (as in the continuation of Example 8.13)

Each RAT, which will contain only multiple-choice and true-false questions, will be conducted as follows:

  1. The questions will be on material that has NOT been covered in class up until that point. You are expected to read material before each test that will help you understand the basic concepts, and the questions on the RAT will determine how well you understand those concepts.
  2. You will get three chances to answer each question asked. If you are sure of your answer, write the same thing three times; otherwise, you may write different answers according to the answers you think are most likely. For example, if the first question is "True or False: The capital of Pennsylvania is Harrisburg," then you should write TRUE three times -- unless you're not sure, that is...
  3. Each student will take the test once as an individual. Each student will submit one individual answer sheet. Individual answer sheets will be graded outside of class.
  4. Once every student has completed the test individually, students will take the exact same test again with his or her assigned group. Each group will submit one group answer sheet. Group answer sheets will be graded in class and returned immediately.
At the end of the semester, each student will receive an Individual RAT Grade and a Group RAT Grade. The Individual RAT Grade is worth 20% of your final grade, and the Group RAT Grade is worth 10% of your final grade. (The lowest individual score and the lowest group score will be dropped for every student.)