Stat 1000: Assignment 4 Tips (Classroom Lecture Sections)
Published: Wed, 03/06/13
My tips for Assignment 5 are coming below, but first a couple of announcements.
Please note that my second two-day review seminar for
Stat 1000 will be on Saturday, Mar. 9 and Sunday, Mar. 10, in room 100 St. Paul's College,
from 9 am to 6 pm each day. This seminar will cover the lessons in Volume 2 of my book.
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 1000
Did you read my Tips on what kind of calculator you should get?
Did you miss my Tips for Assignment 3?
Tips for Assignment 4 (Classroom Lecture Sections A01, A02, A03, etc.)
Don't have my book? You can download a free sample containing Lesson 1 at my website here:
Question 1:
I teach you the difference between a statistic and a parameter in
Lesson 4 of my book and also at the start of Lesson 7. Take a look at
my question 1 in Lesson 7 for an example.
Questions 2 and 3:
These questions deal with the concepts I teach in Lesson 7.
Especially make sure you have practised questions 3 to 7 before
attempting these questions. Always be sure to ask yourself, "Are we
dealing with one individual unit, X? or the mean of n units, x-bar?"
If
we are dealing with just X, can we use the X bell curve? (Have they told
us the distribution is normal?) If we are dealing with x-bar, can we
use the x-bar bell curve? (Have they told us the distribution is normal,
or do we have a large enough sample size to be able to assume the
population of sample means is approximately normal by Central Limit
Theorem?)
Note that question 2(c) is similar to my questions 6 and 7 in Lesson 7.
Question 4:
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 whereX = 0, 1, 2, ... n.
Hints for question 4: 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 5 and 6:
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. Again, if you have an older edition
of my book, your binomial lesson may not have a question 10. In that
case, you will find the relevant example as question 1 in Lesson 10 of
your book.
In general, if you have a Binomial distribution with
parameters n and p, you will compute probabilities using the P(X = k)
formula for binomial distributions. However, if n is large (in the
hundreds, generally), you will use the normal approximation. Which is
to say, you will use a p-hat bell curve.