Stat 1000: Tips for Assignment 7
Published: Sat, 02/18/12
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If you are taking the course by Distance/Online (Sections D01, D02, etc.), click here for my tips for your Assignment 7.
If you are taking the course by classroom lecture (Sections A01, A02, etc.), click here for my tips for your Assignment 7.
There is no Assignment 7 for the Classroom Lecture Sessions.
Study Lesson 5 in Volume 2 of my book, if you have it, to prepare for this assignment.
Question 1:
When you are asked to
list sample spaces, generally you will use a two-way table to visualise
all the possible outcomes. If you are asked to count the number of
things (number of coins, number of successes, etc.), list the sample
space from lowest possible number up. Don't forget that, when counting
the possible number of things, there is always the chance that there
could be 0 things. Some of you are asked about coins. Note, they are
not asking you what denomination the coins are (pennies, nickels, dimes,
etc.). That is irrelevant. They don't care what kind of coins you
might have, just how many and how much money are they worth.
When they ask
you, "Are the outcomes equally likely?", think carefully. Remember, to
be equally likely means that the first outcome you have listed in your
sample space, has the same probability of happening as the second
outcome, etc. Don't think that because the outcomes are equally easy to
list, that makes them equally likely.
For example, if I ask you to the list the sample
space for the possible medals an Olympic athlete might win, I could say
the sample space is {Gold, Silver, Bronze, No medal at all}. Even
though there are four possible outcomes, they are not equally likely!
There is not a 25% chance of winning a Gold medal, for example. It
depends what athlete we are talking about, what event, etc. The mere
fact I have to say "it depends" tells me the outcomes are not equally
likely. Even if the actual medal someone won was randomly determined
and we were assuming every person has an equal chance of winning, if
there were 20 people competing for the medal, there would be only a 1/20
chance they would win gold (since only one person can win gold), and a
17/20 chance they win no medal at all. Of course, some athletes may be
the favourite to win gold and they would then have a much higher chance
than 1/20 of winning.
Of course, some outcomes are equally
likely. For example, if you are flipping a fair coin, or rolling a
fair die, you have every right to say either side of the coin or die are
equally likely to come up.
I think they are quite clear what to do in question 2 which
has you read digits off of Table B. Look carefully at their example for reading Line 101. You look at the first five digits (19223) and record the highest digit you saw (9); look at the next five digits (95034) and record the highest digit (9); 05756, the highest is 6; 28713, the highest is 8; etc. You have to do this a total of 50 times. How many times did you record a 9? How many times did you record an 8? A 7? A 6? etc.
When making your stemplot,
consider all the 9s as 09s, all the 8s as 08s, all the 7s as 07s, etc. The stemplot might look something like this:
Stem | Leaf
0 | 555
0 | 6666
0 | 77777777
0 | 8888888888
0 | 99999999999999999999999999
Trust me, whatever the shape of the distribution of your sample is, that is also likely to be the shape of the population if you had done this an endless amount of times. Ask yourself, will you get 0 the same number of times as you get 9, if you do this over and over again? Will 1 be as common a result as 8?
Questions 3 and 4 are quite similar to my questions in Lesson 5.
Question 5 is dealing with a density curve. Be sure to review the first two questions in Lesson 4 of my book (Lesson 2 if you have an older edition) to better understand what is going on here.
Question 6 is just more probability practise.