Stat 2000: Assignment 3 Tips (Classroom Lecture Sections)

Published: Wed, 03/06/13


 
My tips for Assignment 3 are coming below, but first a couple of announcements.
 
Please note that I am planning on splitting my final exam seminar for Stat 2000 into two days since we will have to cover Lesson 6 in Volume 1 as well as all of Volume 2.  The plan is to meet from 9:00 am to 6:00 pm each day.  Each day will cost $40 or, if you attend Day One, you can attend Day Two for half-price (you will pay a total of $60, in other words).
 
I plan to teach Day One on Easter Sunday, March 31 and Day Two 2 weeks later on Sunday, April 14.  I will send more details and start taking registrations once everything is finalized next week.
 
Did you read my Tips on How to Do Well in this Course? 
Make sure you do:  Tips on How to Do Well in Stat 2000 
 
Did you read my Tips on what kind of calculator you should get?
Tips on what calculator to buy for Statistics
 
Did you miss my Tips for Assignment 2?
Tips for Stat 2000 Classroom Assignment 2
 
If you are taking the course by Distance/Online (Sections D01, D02, etc.), I sent tips for Assignment 2 long ago.  You will find them in my archive:
Grant's Homework Help Archive 
 
Tips for Assignment 2 (Classroom Lecture Sections A01, A02, A03, etc.)
 
Don't have my book?  You can download a free sample containing Lesson 3 at my website here:
Grant's Tutoring Study Guides (Including Free Samples)
 
You need to study Lesson 6: Discrete Probability Distributions (this also includes the Binomial and Poisson Distributions; if you are using a considerably older edition of my book, you may have those two distributions taught in a separate Lesson 7).
 
Extra Tips for Probability
 
I am surprised to see a lot of probability questions on this assignment that are from Stat 1000, so I have included a handout from my Basic Stats 1 study book with a more thorough discussion of making two-way tables and Venn diagrams.  Those of you who have my Basic Stats 1 book, should study Lesson 5: Introduction to Probability.
Excerpts from Grant's Probability Lesson in Basic Stats 1 
 
Conditional Probability
 
Here is another handout explaining the approach to determine a conditional probability:
Conditional Probability Handout
 
Essentially, in conditional probability, when it says "given A" is telling you that we know for sure that event A has occurred, so we are now only interested in outcomes that belong to A.  That becomes the "whole".  P(B|A) wants the fraction of that "whole" that also belongs to B.
 
For example, if you look at my question 18 in the probability handout above, I could add a part (d) that asks, "What is the probability someone is a basketball fan if they are a hockey fan?"  Any probability question that asks, what is the probability of B if event A has occurred, you are doing conditional probability. 
 
We want P(B|H).  I first look through my Venn diagram and find all the bits that belong to H, since we know for sure the person is a hockey fan. There are four bits in the H circle so I add those bits up: 33 + 31 + 8 + 5 = 77%.  Now, I gather all the bits in that H circle that represent people who are also basketball fans.  There are two bits: 8 + 5 = 13%.  Thus, the probability a person is a basketball fan if they are a hockey fan is 13%/77% or .13/.77 = .1688.
 
Here is a couple of extra conditional probability questions I have added to question 4 in my probability handout above:
Question 4 (g) and (h)
 
Here is a couple of extra conditional probability questions I have added to question 16 in my probability handout above:
Question 16 (e) and (f)
 
Additional Tips to help with the Assignment
 
Question 1:
If you are ever asked to decide if a particular situation is binomial or not, remember, to be binomial, four conditions must be satisfied:
(i)  There must be a fixed number of trials, n.
(ii)  Each trial must be independent.
(iii)  Each trial can have only two possible outcomes, success or failure, and the probability of success on each trial must have a constant value, p.
(iv) X, the number of successes, is a discrete random variable where
X = 0, 1, 2, ... n.
Hints for question 1: If you are reading off numbers from a randomly selected row in the random number table, note that every row has 40 digits.  That is like 40 trials looking for whatever digit you may be looking for.  What is the probability that, at any moment on the table, the next digit is a 0, or a 1, or a 2, etc.?
 
If you are selecting objects, are you sampling with replacement (independent trials) or without replacement (dependent trials)?
 
Question 2 is very similar to my question 18 in the Extra Help with Probability handout I have given you. I certainly recommend you make a three-circle Venn Diagram to solve this problem.
 
Question 2 (h) and (j) are examples of conditional probability.  I also discuss conditional probability in the handout, above.
 
Do you notice what kind of method you need to use to solve question 2 (k) and (l)?
 
Question 3 is a two-way table problem similar to my question 13 in the handout above. 
 
For question 3(d), go through each outcome in your sample space and determine the value of X first.  For example, one of the outcomes in the sample space you listed in part (a) would be "13" meaning X1=1 and X2=3 (you might write it as 1:3 or 1;3 or something so that it is not mistaken for thirteen).  Then X=2 since |X1 - X2| = |1 - 3| = |-2| = 2.
 
Note that question 3(e) is a conditional probability.
 
Questions 3(f) and (g) are using the formulas for mean and variance I show you at the start of Lesson 6 (questions 1, 2 and 3).
 
Question 4 is very challenging.  You have two normal distributions, X1 and X2.  You can use the properties of mean and variance I teach at the start of Lesson 4 to work out the mean and variance of X1 + X2.  Since X1 and X2 are both normal distributions, X1 + X2 is also normal.  Part (b) wants X1 < X2 which can also be written X1 - X2 < 0.  Again, you can find the mean and variance of X1 - X2. Of course, to change your score into a z-score, you will have to use the standardizing formula you first learned in Stat 1000, z = (x - mu)/sigma or z = (x - μ)/σ.
 
Question 5 is obviously binomial.
 
Question 6 is similar to a question I teach in Lesson 6 in the "Hypothesis Testing Revisited" section.  Note that you can use Table C to solve the probabilities more quickly.
 
Questions 7 and 8 are obviously Poisson Distribution questions similar to my examples in Lesson 6.