Stat 2000: Assignment 1 Tips (Classroom Lecture Sections)
Published: Wed, 02/06/13
My tips for Assignment 1 are coming below, but first a couple of announcements.
Please note that my first review seminar for
Stat 2000 will be on Feb. 24 (one week before the midterm exam). Unfortunately, that means the seminar is the weekend at the end of the week-long Midterm Break, but it is out of my hands. This seminar will cover the lessons in Volume 1 of my book.
For more info about the seminar, and to register if you have not already done so, please click this link:
I am also taking registrations for all my midterm exam
prep seminars (Calculus, Linear Algebra, and Statistics). Please click this link for more info and to register, if
you are interested:
Make sure you do: Tips on How to Do Well in Stat 2000
Did you read my Tips on what kind of calculator you should get?
If you are taking the course by Distance/Online (Sections D01, D02, etc.), I sent tips for Assignment 1 long ago. You will find them in my archive:
Tips for Assignment 1 (Classroom Lecture Sections A01, A02, A03, etc.)
Don't have my book? You can download a free sample containing Lesson 3 at my website here:
You need to study Lessons 1, 2 and 3 in my book (if you have it) to prepare for this assignment. Do not attempt to do this assignment until you have studied ALL of these lessons.
For the JMP 10 part of the assignment, here are some tips:
If you have not done so already, you need to download JMP to
your computer. Here is the direct link where you can get it (you need
to know your UMNET ID and password):
Once you have installed JMP 10 and opened it, you are shown a
menu with various buttons to click. You will almost always click "New
Data Table" to enter new data. That is the icon on the far left of the
top toolbar (it looks like a tiny little spreadsheet with a yellow star,
point your mouse at it and you should see the label "New Data Table"
pop up.
In the rare event they have given you a
JMP file with the data already entered in it, you will simply open that
file which would probably already open JMP for you. Just click the
"Open" icon on the same toolbar as the "New Data Table" icon, or, if you
already see the file in the "Recent Files" screen, simply double-click
that. If you happen to
enter data in yourself and save the file (a good idea), you can select
"Open" to open up the saved file.
Questions 2 and 3 are a good run-through of errors and power in hypothesis testing as I teach in Lesson 3. Make sure you round off
to the required number of decimal places. Don't just trim your
answers. For example, if you get 1.23456 and you are rounding to four
decimal places, you would round that off to 1.2346. They do not make it
clear, so I would assume that once you have computed the critical value
for x̅ (what I call x̅*), and you have entered it into the
relevant box, use this rounded off value for any future calculations.
You may want to clarify with the prof as to whether they expect you to
use the rounded off numbers for future calculations in the problem, or
if they want you to use the non-rounded values.
Question 4 is more of the same. To do part (c) more easily, read my
part of Lesson 3 talking about "The Relationship between the Alternative
Mean and the Power of a Test."
Question 5 is just a matter of typing your
explanations into the box provided. This is like what I discuss at the
start of Lesson 3 where the Type I error is "saying someone does not
have cancer when they actually do." Note that they also want you to describe the consequences of each error.
Question 6 is a good run-through of hypothesis testing as I teach in Lesson 2 of my book.
Question 7 should be done both by hand (i.e. just using your calculator) and with JMP.
First, put your calculator in Stat Mode (as I show in Appendix A of
my book for various makes and models of calculator) and find the mean
the data. (You don't need to calculate the standard deviation since
they have given you the population standard deviation.)
Here is a link to a
digital copy of that appendix:
They apparently want you to answer all the questions in the
text box provided at the bottom. You can simply type in all your
answers, or you could type them into a Word document (or whatever word
processor you use) and then save that document as a PDF and upload it
into the textbox afterwords. I would suggest you use a word processor
since you can then also add the JMP stuff to it as well and upload it
all later, rather than type a bunch of stuff in the box and also upload a
JMP file.
7(a) is fundamental. See my discussion in Lesson 1 on why Inferences for the Mean are robust.
7(b) is using an unusual level of
confidence. See my question 10 in Lesson 1 for an example. Note that
they want you to explain how you get z*.
7(c) is standard. I show you how to interpret a confidence interval in Lesson 1.
Note that you already know the z* critical value for 7(d).
You used it in part (b). You can use the Equation Editor in Word to
write the formula work you are doing, or you can just find the formula
via Google and copy and paste it into your document. Don't feel
obligated to make your calculations look pretty, just use words to
describe what you are doing, if you prefer, or just type the numbers
like so: "z = 6 - 10 divided by 3/square root of 6" (my numbers are just
made up, of course).
7(e) and (f) are standard P-value stuff. I show you how to interpret a P-value in Lesson 2.
7(h) is the concept of using confidence
intervals to test hypotheses. Look at my question 13(d) in Lesson 2
for a discussion of this concept.
7(g):
First, enter the data into JMP manually:
Click the "New Data
Table" icon on the toolbar at top left in the JMP home screen. You are
automatically taken to an empty spreadsheet with one
column. Double-click "Column 1" and change its name to "Wait Time", or
right-click "Column 1" and select "Column Info" and type in the name
"Wait Time" and click OK.
Now just type in the various Wait Time values in the cells using
your "Tab" or down arrow button to move to each proceeding cell. You
can also hit "Enter" after each piece of data to enter it and move to
the next cell.
Once you have entered all the data down your columns, you are ready to test the hypothesis and make your confidence interval. In the toolbar at the
top, select Analyze then select Distribution. In the "Select Columns" part of the pop-up window, click the column you
want to analyze ("Wait Time" in this case) to highlight it, and click the Y, Columns
button. You should see the "Wait Tie" column appear in the section to the right of the "Y, Columns" button. Click OK.
It now opens yet another pop-up window called "Distributions"
where a histogram should appear. Your histogram appears sideways.
To get JMP to make confidence intervals and test hypotheses for the mean:
To get a confidence
interval, click the red triangle next to variable "Wait Time"
directly
above the histogram to get a drop-down list and select "Confidence
Interval". In the pop-up window that appears, select "Other" (even if
the level of confidence you desire is in the list) and type in the
level
of confidence you want (in decimal form, so 97%, for example, is 0.97). Make sure
"Two-sided" is selected. You are given a value for sigma, the
population standard deviation, so click the "Use known Sigma"
checkbox.
Click OK. You will get another pop-up window where you can type in
your
known value for sigma (20, in your case). A Confidence
Intervals table will appear in your output screen at the bottom. Your
lower and upper limits are shown under "Lower CI" and "Upper CI" in the
Mean row. These answers should agree with your computed answers in part
(b) above.
To
test a hypothesis, click that same red triangle you used to make a
confidence interval and select "Test Mean". Type in the value the null
hypothesis believes the mean to be (60, in your case) and type in the known value of sigma
(20 in your case) in the box that says "Enter the True Standard Deviation to do a z-test ...". Click OK. A "Test
Mean = Value" table appears in your output where, among other things,
JMP gives you the test statistic and three probability values. Those
three probabilities are the P-value for the three possible alternative
hypotheses. JMP will use a z statistic since you gave it a sigma value.
Prob > |z| is the two-tailed P-value (that is the one you want).
Prob > z is the upper-tailed P-value.
Prob < z is the lower-tailed P-value.
JMP's answer for the P-value should agree with what you calculated yourself in part (e).
Press "Alt" on your keyboard or click the thin blue line that
is near the top of the window to get the toolbar icons to appear. Select
the icon that looks
like a fat white cross or plus sign "+". This is your "Selection"
tool. Your mouse cursor should now have changed from an arrow to that
white cross. Click the title bar that says "Distributions" at the top
of the output and that should select the entire output (histogram,
Summary Statistics, etc.). Right-click and select Copy. You can then
paste this into the document you were typing all your previous answers
into.
Question 8 is basically a repeat of question
7, but now you are using t. I assume that they want you to use the
values for the sample mean and standard deviation they provided to
answer part (a). Note, in part (c)
enter the lower bound of the P-value first. For example, if you have
established that the P-value is between .02 and .01 (I am just making
those numbers up and have no idea what you will determine), type "0.01"
in the first box and "0.02" in the second box.
For 8(e), follow exactly the same JMP
steps I outlined in question 7 above to do the JMP in this question.
Make a New Data Table, naming the column "CO". This time,
you do not have a value for sigma, so leave the "Enter the True Standard
Deviation ..." box in the Test Mean screen empty.
Again, you are given a choice of three probabilities "Prob
> |t|," "Prob > t," and "Prob < t" in the Test Mean = Value
part of the output. That gives you the two-tailed, upper-tailed, and
lower-tailed P-value, respectively. You should know which of those is
appropriate for the hypothesis test you have been doing.
Question 9 is yet another hypothesis test as I teach in Lesson 2. Thankfully, no JMP required.