Stat 1000: Some handy summary handouts for Units 6 to 11

Published: Sun, 04/09/17

Here are some extra notes I wrote to help you organize the key problems covering the concepts in Units 6 to 11 of the course.  Those units correspond to Lessons 6 to 11 in my book, but omit Lesson 10 in my book; they have removed that lesson from the course.  Be clear, my Lesson 10 is not their Unit 10.  Their Unit 10 has already been taught in my Lessons 8 and 9.  They are just introducing t in Unit 10, something I already did in Lessons 8 and 9.
Confidence Intervals
Remember, if ever asked to make a confidence interval, there are three possible formulas you will use depending on whether you are asked to make:
  1. A confidence interval for the MEAN where σ is known (so we use z*).
  2. A confidence interval for the MEAN where σ is unknown (so we use t* with df=n-1).
  3. A confidence interval for the PROPORTION (we always use z*), this formula is included on the exam's formula sheet.
Hypothesis Tests
Remember, if ever asked to test a hypothesis, there are three possible test statistic formulas you will use depending on whether you are asked to test a hypothesis about:
  1. A hypothesis for the MEAN, μ, where σ is known (so we use z).
  2. A hypothesis for the MEAN, μ, where σ is unknown (so we use t with df=n-1).
  3. A hypothesis for the PROPORTION, p, (we always use z), this formula is included on the exam's formula sheet.
Binomial Problems
Remember, if you ever identify that you are given n and p, then you can bet you have a binomial problem.   There are two different methods to solve binomial problems (note that the formulas used in both cases are given on your exam's formula sheet):
  1. When n is small (n is about 20 or less) is the classic binomial problem as taught in Lesson 6 of my book.  List X=0,1,2,...n and find the probability of some value k using the formula.
  2. When n is huge (n is at least 100) is too slow to solve using the classic method (#1 above).  Instead we approximate the probability using the p^ bell curve because it is reasonable to assume that the sample proportion, p^, is approximately normal.  (Technically, if there is any doubt, we check np and n(1-p) and confirm they are both 10 or greater.)
Sample Size Problems
Remember, if you are asked "how large a sample should we select" or the like, there are two different sample size formulas.  The cheesy trick to know which one to use is the fact that one of these formulas requires a σ and one does not.  If they have given you a σ, you can bet it is the formula that has σ in it.  If they have not given you a σ, you can bet it is because you don't need one, you are using the other formula.
  1. The sample size formula when estimating a MEAN (this formula requires a σ, and it must be memorized).
  2. The sample size formula when estimating a PROPORTION (this formula does not require a σ, and it is included on your exam's formula sheet).