Stat 1000: Assignment 10 Tips (Distance/Online Sections)
Published: Fri, 03/22/13
My tips for Assignment 10 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 9?
If you are taking the course by Classroom Lecture (Sections A01, A02, etc.), there is no Assignment 10.
Tips for Assignment 10 (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 be using Table A and Table D while learning Lesson 8
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 testing your hypothesis. I would
assume, at this stage, you are likely to be given σ most of the time.
Question 1 is basic P-value stuff as taught in Lesson 9. See my examples before question 6. You may find it easier to visualize if you convert the P-value and level of significance into a percentage before making a decision.
Questions 2 and 3 are a good run through of the 5 steps to test a hypothesis.
Question 4: Requires use of JMP.
To make a confidence interval for the mean using JMP:
Select and copy the data. Click "New
Data Table", then select "Edit" then "Paste with Column Names". Now
select "Analyze", "Distribution" and highlight "radon" and click "Y,
Columns", then click OK. You are now looking at a histogram and stuff.
Click the red triangle next to "radon" then select "Confidence
Interval" from the drop-down list. Select "Other" to get a pop-up menu.
It probably already has 0.95 typed in (for 95% confidence interval),
but, if not, be sure to type in 0.95. Make sure you click the box saying "Use known Sigma".
Click "OK" and you will then get a pop-up menu to type in the sigma
value. I believe σ = 9 in your case. Click "OK" and JMP gives you the
Confidence Interval at the bottom of the printout.
To test a hypothesis for the mean using JMP:
You
should already be in the output screen having done the confidence
interval in part (a). You are now looking at a histogram and stuff.
Click the red triangle next
to the variable and select "Test Mean" from the drop-down list. Enter in
the
population mean as stated in your null hypothesis and enter in the given population standard
deviation, sigma. 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. Please understand that it is irrelevant to JMP what your level of significance is. You do not enter that anywhere. JMP leaves it up to you what decision to make based on whatever level of significance you are using.
Note that when JMP gives you:
"Prob > |z|" JMP is giving you the two-tailed P-value,
"Prob > z" JMP is giving you the upper-tailed P-value,
"Prob < z" JMP is giving you the lower-tailed P-value.
It is up to you to know what your alternative hypothesis is, and so what the correct P-value is. Question 5:
Follow the same steps as done in question 4 to test the
hypothesis about IQ. Just make sure you make IQ your Y Column. After
you have done "Test Mean" in JMP (and entered the mean for your null
hypothesis and the given sigma), select, copy and paste the printout
into Word (or whatever word processor you use). Remember, to select the
JMP printout, press "Alt" to see the toolbar and choose the "Selection" tool from the (looks like a white cross).
Note that JMP does all your work for you for part (a).
In your Word document, make sure you state the hypotheses, the test
statistic (as computed by JMP), the P-value (as computed by JMP), and
your conclusion.
Make sure you read my section on P-values to learn how to properly
interpret your P-value for part (b). I give you a couple of examples in my question 6.
In question 6, remember the
note I write after my question 4 talking about statistical significance
versus
practical significance. Also, remember the Law of Large Numbers taught
in
Lesson 7 of my book. The key concept is, that as n, the sample size,
gets larger, the sample mean will come closer and closer to the true
mean, mu. Put another way, the larger the sample size, the closer your
statistic will come to the TRUTH. If the truth is that the null
hypothesis is correct, then you are likely to get a larger and larger
P-value, and so you would not be able to reject the null hypothesis.
However, if the truth is that the null hypothesis is wrong, then you
would expect that larger and larger samples would more clearly prove
that Ho is wrong, meaning you would get a smaller and smaller P-value,
and stronger evidence to reject Ho.