Stat 1000: Assignment 11 Tips (Distance/Online Sections)
Published: Thu, 03/28/13
My tips for Assignment 11 are coming below, but first a couple of announcements.
Please note that my final two-day review seminar for
Stat 1000 will be on Saturday, Mar. 30 and Sunday, Apr. 7 (eight days later), in room 100 St. Paul's College,
from 9 am to 6 pm each day. This seminar will cover the lessons in Volume 3 of my book. I expect to also have time on Day Two to go through a Sample Final Exam.
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 10?
If you are taking the course by Classroom Lecture (Sections A01, A02, etc.), there is no Assignment 11.
Tips for Assignment 11 (Distance/Online Sections D01, D02, D03, etc.)
Don't have my book? You can download a free sample containing Lesson 1 at my website here:
You will also need to study Lesson 10: Comparing Two Means. (You only need
to study the first half of Lesson 10 where I teach matched pairs, you
do not need to study the pooled two-sample method; they don't teach the
two-sample method in the distance course. Those of you with older
editions of my book, have the matched pairs lesson at the end of lesson 9.)
You will be using Table A and Table D while learning Lessons 8
and 9, and doing this assignment. Here is a link where you can
download those tables if you have not done so already:
First, be sure
to note whether a question gives you σ, the population standard
deviation, or s, the sample standard deviation. That dictates whether
you will use z or t when making your confidence interval or testing your hypothesis. I would
assume, at this stage, you are likely to be given s most of the time.
Question 1 is standard confidence interval stuff using t* as I show in Lesson 8.
In question 2, you
are asked for the standard error of the sample mean, not the standard deviation.
When they ask for S(x-bar), they are actually asking for SE(x-bar). I
discuss the Standard Error of the sample mean in
Lesson 8 of my book. It is s, your sample standard deviation (as
computed using the Stat mode in your calculator) divided by the square
root of n.
Note the margin of error of
any confidence interval is everything that comes after the +/- in the
appropriate formula. Which is to say, in this case, it is t* multiplied
by the Standard Error you just entered in part (a). Note that you are
told to use the answers in part (a) rounded to two decimal places when computing the margin of error in part (b).
Question 3
Look at my examples 8, 9 and 10 in
Lesson 9 to understand how to put bounds on a P-value if you are using t. BE
CAREFUL! In Web Assign, when you are entering the critical values and tail
area bounds into your boxes always put the smaller value in the left box
and the larger value in the right box because the < signs demand
that. When you are asked if the result is significant, they are asking you would you reject Ho.
Question 4
This is a matched pairs
problem. Study my questions 1 and 2 in Lesson 10 (or study the last two
questions of Lesson 9 if you have an older book) to understand how to
do
hypothesis tests for matched pairs.
To use JMP to do a matched
pairs test, copy and paste the data into New Data Table the usual way
then select "Analyze", "Matched Pairs". Be sure to read the
entire problem to
determine if they have specified the order they want you to subtract.
You
will see in part (c), they want JMP to do "op1- op2". Therefore, in the
Matched Pairs pop-up menu, select "op2" first,
then click "Y, Paired Response", then select "op1" and click "Y, Paired
Response". Thus, in the Y, Paired Response window, you would
see "op2"
listed above "op1". JMP always does Second - First, so whichever is
listed
second in that window will be the front of the subtraction. Click OK.
The output then gives you all you need. The "t-Ratio" is your test
statistic, and the three probabilities are the three P-values for the
two-tailed, upper-tailed, and lower-tailed tests. You also are given
the confidence interval you desire. If JMP does not subtract in the
correct order, repeat the steps and change the order you select "op1"
and "op2" in the Matched Pairs pop-up window.
After
using JMP to do the problem, I also suggest you do it by
hand since a question like this is always a possible exam question.
However, by hand, the best you can do is put bounds on the P-value,
whereas Web Assign requires an exact P-value.
Question 5
To use JMP: Select and copy the data and paste it into JMP
the usual way. Note that the question only wants you to examine the
red
flowers.
Therefore, be sure you only select and copy the data for the red
flowers. That will also mean you will need to type in the names for
the
columns yourself at the top. Alternatively, you could select and copy
all the data, then delete the rows in the JMP spreadsheet that do not
have red flowers. (To delete rows, hold down the "Ctrl" key on your
keyboard while you select all the rows you wish to delete. Then select
"Rows" in the toolbar at top, and select "Delete Rows.")
Select "Analyze, Distribution" and make "length" the "Y
Column " and click OK to get the Histogram and stuff. Click the red
triangle next
to the variable and select "Test Mean" from the drop-down list. Enter in
the
mean from your null hypothesis (given in part (c) of the problem). Click "OK" and JMP gives you the
hypothesis test at the bottom of the printout. Look
at my questions 13 and 14 for examples of how to read this printout.
Remember:
Prob > |t| is the two-tailed P-value
Prob > t is the upper-tailed P-value
Prob < t is the lower-tailed P-value
You can now select, copy
and paste your output to a Word document or similar ready for upload as usual.
In part (b), when they ask is it appropriate to use the
method, they are getting at what you have discovered about the possible
shape of the population according to your sample's histogram. Be sure
to read my section about "Inferences about the Mean are robust" and what
we conditions are necessary for different sample sizes in Lesson 8 just
before I do question 1.
When
they say "show all your steps", that does not mean you have to show
how
the calculations are being done, just go through the 5 steps and list
what you have come up with for each step, using JMP's
numbers wherever appropriate. Which is to say, state your hypotheses,
list the test statistic as given by JMP, list the P-value as given by
JMP, then write your conclusion.
For part (d), make sure you read my section on P-values to learn how to
properly interpret your P-value and look at my question 6 for some examples. All that is required is one or two sentences.
Do not think you have to write an essay, and don't think you have to really
write something that a "layman" will understand. A layman is never going to
understand a P-value, even if you spent three pages trying to explain
it.
Once you have written all your answers, save your document as a PDF and upload it to WebAssign.
Question 6 is just more practise at the
concepts in Lessons 8 and 9. You all get different types of questions
here, so I can't be more specific.