Stat 1000: Assignment 4 Tips (Classroom Lecture Sections)
Published: Wed, 11/07/12
My tips for Assignment 4 are coming below, but first a couple of announcements.
Please note that my second midterm exam prep seminar for
Stat 1000 will be on Sunday, Nov. 4, in room 100 St. Paul's College,
from 9 am to 9 pm . For complete info about the seminar, and to register if you have not done so already, click this link:
I am also offering seminars in Calculus, Linear Algebra, and Stat
2000 in the coming weeks. You can get info about those seminars here:
Make sure you have read my Tips on How to Do Well in this Course
Did you miss my Tips on what kind of calculator you should get? Click here
If you are taking the course by Distance/Online (Sections D01, D02, etc.), click here for my tips for your Assignment 9.
Tips for Assignment 4 (Classroom Lecture Sections A01, A02, A03, etc.)
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)?"
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.