Stat 2000: Tips for Assignment 4
Published: Wed, 11/21/12
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Stat 2000 will be on Sunday, Dec. 2, 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:
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1000 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
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Did you miss my tips for Assignment 3? Click here
Tips for Assignment 4
You need to study Lesson 7: Inferences about Proportions (if you are using an older edition of my book, this may be Lesson 8). You also will need to study the first half of Lesson 8: Chi-Square Tests (up to the end of question 4, you do not need to study the Goodness-of-Fit Test at this time).
Question 1 is very similar to my question 1(c) and
(d) in Lesson 7. Note, as I discuss back in Lesson 6, question 7, a
fraction is another way of giving you a value for p.
Question 2 is standard stuff, like my questions 6
to 8 in Lesson 7. Note that part (b) is talking about the
Inverse-Square Relationship for sample size which I introduced way back
in Lesson 1, question 8.
Question 3 is a good run through of confidence
intervals and hypothesis testing as I teach in Lesson 7 (see my
questions 2 and 3). Parts (f) to (h) require an alpha/beta table. Note that
you will need to use the z* critical value (part (f)) to compute p-hat*, the
critical value for p-hat where you will reject Ho (the p-hat decision
rule) (part (g)). We derive p-hat* from the standardizing formula for p-hat bell
curves.
Question 4 is very similar to my questions about
confidence intervals and hypothesis tests for the difference between two
proportions taught in the latter half of Lesson 7. Part (g) introduces
the concept i teach in my question 4 in Lesson 8 (Chi-Square Tests).
Note that you don't really have to do any work for part (g) if you apply
the concept that relates two-proportion z tests to 2 by 2 Two-Way
Chi-Square analysis.
Question 5 is just more practise at interpreting a confidence interval for a proportion and the P-value for testing the difference in the two proportions. I showed you how to interpret a confidence interval for a mean way back in Lesson 1. Your interpretation for a proportion is much the same. I showed you how to interpret a P-value back in Lesson 2. Just be careful about what the null hypothesis is.
Here is how to do Contingency Tables (2-Way Tables) in JMP:
Click New Data Table. You will need a total of three columns.
Double-click Column 1 and name it "Course" and change the Data Type to
"Character" and the Modeling Type to "Nominal". Double click the space to the
right of the Course column to create a new column. Name that column "Grade" and
change the Data Type to "Character" and the Modeling Type to "Nominal". Double
click the space to the right of the Grade column to create a new column. Name
that column "Count" and keep the Data Type as "Numeric" but change the Modeling
Type to "Nominal".
Make sure that you have the correct Data Type and Modeling Type for each of these three columns as I outline above!
Each row in the JMP data table is used to
enter the information for a particular cell of the two-way table. The
first row
will represent the 1,1 cell; the second row will represent the 2,1 cell;
etc.
For example, your 1,1 cell gives you the observed count for the people
who took Biology and got an A+. In the JMP data table, in row 1
type "Biology" in the Course column, "A+" in the Grade column, and type
the given observed count in the "Count" column. Type the info for
the 2,1 cell
into the second row of your JMP table. That is the observed count for
the people who took Biology and got an A, so you will type
"Biology" in the Course column, "A" in the Grade column and the
observed count in the Count column. In the third row you will type Biology in the Course column, B+ in the Grade column,
and the cell count in the Count column, the observed count for the 3,1 cell in the Count column. Continue in this fashion all the way to
the 24th row where you will type "Physics" in the Course column,
"F" in the
Grade column, and the observed count for the 8,3 cell in the
Count
column.
You will notice that the first two columns
of the JMP table are used to specify which row and column of the two-way table
you are talking about, and the third column enters the observed count for that
particular cell.
Once you have entered in all the observed
counts, select Analyze, Fit Y By X. Select "Course" and click "Y,
Response",
select "Grade" and click "X, Factor", and select "Count" and click
"Freq".
Click "OK". Click the red triangle next to "Contingency Analysis of
Grade by Course " at the top and deselect "Mosaic Plot" to remove that
from the output.
You now see a Contingency Table (or two-way table) and the "Tests" below
it.
(If your two-way table has the rows and columns the wrong way round
compared to what the question has, that doesn't really matter, but you
can fix that by changing which column you called X and which you called
Y.
Click the red triangle next to Contingency Table and make sure that all that is
selected is "Count", "Expected" and "Cell Chi Square" to display those values in
each cell of the table. Note the Pearson ChiSquare is the test statistic for
the problem (in the last row of the "Tests" output) and the Prob>ChiSq is the
P-value for that test.
When they ask in part (c) which four cells contribute most to the test statistic, they are asking which four cells
have the largest chi-square values.
Select File in the JMP toolbar and Save As to save the JMP printout as a PDF file then upload it to the HTML editor. Be sure to answer the rest of their questions in the box provided.
Question 7 is a classic Chi-Square Two-Way table problem similar to my questions 1 to 3 in Lesson 8.