Stat 1000: Tips for Assignment 8

Published: Mon, 03/05/12

 
Please note that my second midterm exam prep seminar for Stat 1000 will be on Saturday, Mar. 10, in room 100 St. Paul's College, from 9 am to 9 pm . 
Please click this link for more information about the seminar and to sign up if you are interested:
Grant's Stat 1000 Exam Prep Seminars 
 
If you ever want to look back over a previous tip I have sent, do note that all my tips can be found in my archive.  Click this link to go straight to my archive:
Grant's Updates Archive
 
Did you miss my Tips on How to Do Well in this Course? Click here
 
Did you miss my Tips for Assignment 7? Click here
 
If you are taking the course by Distance/Online (Sections D01, D02, etc.), click here for my tips for your Assignment 8.
 
If you are taking the course by classroom lecture (Sections A01, A02, etc.), click here for my tips for your Assignment 8.
 
Tips for Assignment 8 (Sections A01, A02, etc.)
 
 There is no Assignment 8 for the classroom lecture sections.
 
Tips for Assignment 8 (Distance/Online Sections D01, D02, etc.)
 
You will need to study Lesson 6: The Binomial Distribution and Lesson 7: The Distribution of the Sample Mean in my study book to prepare for this assignment. These lessons may be in reverse order if you have an old edition of my study book.
 
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.
 
Question 2:
If you are solving a binomial problem, and they ask you to compute a mean and/or standard deviation, read carefully.  Do they want the mean of X? or do they want the mean of p-hat, the sample proportion?  Be sure to study the sections about the Distribution of X and the Distribution of p-hat in my Binomial Distribution lesson (Lesson 6 in my new edition, Lesson 7 in older editions).  Take a look, especially, at question 10 of that lesson as a good run through of these concepts.
 
Question 3:
Questions that give you μ and σ are undoubtedly dealing with bell curves.  Make sure you have studied my lesson on the Distribution of the Sample Mean (Lesson 7 in the new edition, Lesson 6 in older editions).  Always be very careful to note, are they asking you for the probability of one individual value (X)?, or are they asking you for the probability of the average or mean of n values (x-bar, the sample mean)?  If you are dealing with X, use the X standardizing formula.  If you are dealing with x-bar, use the x-bar standardizing formula.
 
Also, note that you can only do probabilities for X in these cases if you are specifically told that X is normally distributed.  Otherwise, there is no X-bell curve, and the probability is unknown.  However, thanks to the Central Limit Theorem, we can always assume there is an x-bar bell curve (the sample mean is normally distributed), as long as n is large.
 
In question 3, part (b), how big a sample size n do you need to reduce σ(x-bar), the standard deviation of x-bar, down to a certain amount?  You can solve that by some algebra, but I suggest you just use trial and error.  Try n = 10, for example, and see if that works.  If not try n = 20 or something.  Play the Price is Right Clock Game.  Try higher n's, lower n's until you home in on the n that works.  With a calculator, I contend you can arrive at the correct answer quite quickly.  Those of you who feel comfortable with algebra are certainly welcome to solve the problem that way.
 
Note, in Question 3, parts (c) and (d), it appears you do not have enough info to solve the problem because they have not given you a value for μ, the population mean.  That is because the actual value is irrelevant.  If you ever come across a problem like this, pretend that μ = 0, and then be careful to draw a picture and shade the region they describe.  Proceed to compute your z-score, etc.  Try it again, but this time using μ = 10 and making the appropriate adjustments to your bell curve and shade the region.  You will discover you get the exact same z-score.  This works no matter what you use for μ.  That's why the easiest choice is μ = 0.
 
Question 4:
Again, be sure to look at my question 10 in my Binomial Distribution lesson to understand how to approach this question.  You will need the standardizing formula for p-hat bell curves that I use in question 10(c).
 
Question 5 is just more of the same stuff from Lessons 6 and 7 in my book (different people get different questions).  Some of you get a question where they give you the mean and variance and ask you what n and p are.  Just use trial and error.  It is a multiple choice question. Use the given n and p from each choice and sub it into the formulas to see if they produce the required mean and variance.  There is no need for algebra.
 
Question 6 uses the Sampling Distribution simulator at Rice Virtual Lab in Statistics.  Read Carefully.  They first have you play around with it using a Normal Distribution.  But, the actual questions they ask want you to use a "Skewed Distribution".  Note that, in the top left corner, you are given the mean and standard deviation of the population (μ and σ).  The various questions you are being asked are about the distribution of the sample mean.  Compare the answers for the mean and standard deviation of x-bar that the applet is giving you (next to the third histogram) with the theoretical values you expect if you computed the mean and standard deviation of x-bar using the formulas I give you in "The Distribution of the Sample Mean" lesson of my book.  This applet is illustrating the same concepts I discuss in Figures 1 and 2 in Lesson 7.  The fact is, you can answer all the questions they ask without using the applet.  Just use your formulas for the mean and standard deviation for x-bar.  All you need is the μ and σ given at the top left corner for the Skewed Distribution in the applet.  You should notice that μ = 8.08 and σ = 6.22 for the Skewed Distribution.