Stat 2000: Tips for Assignment 4
Published: Tue, 11/15/11
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If you are taking the course by classroom lecture (Sections A01, A02, etc.), click here for my tips for your 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.
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 which I introduced back in Lesson 1, question 8.
Question 3 is a good run through of hypothesis testing as I teach in Lesson 7 (see my question 3). Part (f) requires an alpha/beta table. Note that you will need to use the z* critical value to compute p-hat*, the critical value for p-hat where you will reject Ho (the p-hat decision rule). We derive p-hat* from the standardizing formula for p-hat bell curves. Click this link to see how to find the critical value for p-hat:
Question 4 is very similar to my question 4 in Lesson 8 (Chi-Square Tests), as well as incorporating confidence intervals as taught in my Lesson 7.
Question 5 requires the use of JMP.
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 "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 "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 "Count" and keep the Data Type as "Numeric" but change the Modeling
Type to "Nominal".
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 1,2 cell; etc.
For example, your 1,1 cell gives you the observed count for the A+ students who
took Biology. In the JMP data table, in row 1
type "A+" in the Grade column, "Biology" in the Course column, and type
the given observed count, 20, in the "Count" column. Type the info for the 1,2 cell
into the second row of your JMP table. That is the observed count for the A+ students who took Chemistry, so you will type
"A+" in the Grade column, "Chemistry" in the Course column and the
observed count, 23, in the Count column. In the third row you will type A+ in the Grade column, Physics in the Course column, and 17, the observed count for the
1,3 cell in the Count column. Continue in this fashion all the way to the
24th row where you will type "F" in the Grade column, "Physics" in the
Course column, and 20, 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.
Click the red triangle next to Contingency Table and make sure that all that is
select 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) what four cells contribute most to the test statistic, they are asking which four cells
have the largest chi-square values.
Question 6 has you do a Two-Way Table by hand, as I teach in Lesson 8, questions 1 to 4.
There is no distance/online course for Stat 2000 this term.