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Final Exam Prep Seminar is Good Friday, April 3
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Did you read my tips on how to study and learn Stat 2000? If not, here is a link to those important suggestions:
Did you read my Calculator Tips? If not, here is a link to those important suggestions:
Study Lesson 8: Inferences about Proportions (if you are using an older edition of my book, this may be Lesson 7). You also will need to study the first half of Lesson 9: Chi-Square Tests (up to the end of question 4, you do not need to study
the Goodness-of-Fit Test at this time).
Remember my advice in the tips above. Don't start working on the assignment too soon. Study and learn the lesson first, and use the assignment to test your knowledge. Of course, always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment. Learn first, then put your learning to
the test.
Exception: Always do any JMP stuff open-book. Have my tips in front of you, and let me guide you step-by-step through any JMP stuff. JMP is just "busy" work. The sooner you get it done and move on to productive things like understanding the concepts and interpreting the JMP outputs, the better off you will be. Don't have my book or audio lectures? You can download a free sample of my book and audio lectures containing Lesson 3:
A Warning about StatsPortal
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Make sure that you are using Firefox for your browser. Don't even use Internet Explorer. It actually also has some glitches in the HTML editor boxes.
Do note that every time you exit a question in StatsPortal, the next time you return to it, the data may very
well change. Do not press the "back-up" button on your browser in a question. That, too, will change the data. When you are prepared to actually do a question, open the link, keep it open, and do not close it until you have submitted your answers. Be sure to press "Save Answers" once you have done any calculations and entered any information to ensure the data does not change and force you to start over again.
After you submit the answer to a question,
if you have been marked wrong on any parts, be sure that you write down the correct answers before you exit the screen (or grab a screen shot). To try a second attempt at the question do not click the link to the question again, that will change the data and you will have to start all over again. Also, DO NOT click "try again" or make a "second attempt." That will also reset the data.
Instead, exit back to the home screen where they show the links
for all the different questions on the assignment. Where it shows the tries for a question on the right side of your screen, you should see the "1" grayed out, showing that you have had 1 attempt. Click the number "2" to get your second attempt with the same data. That way you can enter the answers you already know are correct and focus on correcting your mistakes.
You should also have already downloaded the JMP statistical software which was
provided with either one of the course options for StatsPortal as mentioned in your course outline.
Make sure you have gone through Assignment 0 completely to learn how to use the interface. I also suggest you print out a copy of question 8 in Assignment 0 (Long Answer Questions - Part 3) so that you have the steps for saving and uploading files into the HTML editor in front of you.
Question 1: Sample Proportions
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This is very similar to my question 1(c) and (d) in Lesson 8. Be careful to note which is the true proportion, p, and which is the sample proportion p^.
Be careful that you don't lose accuracy by rounding off too
much. I suggest you round off to no less than 5 or 6 decimal places while computing things like the standard deviation of p^ to ensure that you get accurate z-scores. Better yet, store exact answers in memory in your calculator.
Question 2: Olympic Probabilities
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This is standard sample size stuff, like my questions 6 to 8 in Lesson 1. I think they screwed up here, because you would have expected this to be the proportion sample size stuff from Lesson 8, but
instead it is just a rehash of the mean sample size stuff they already did in Assignment 1.
Note that part (c) is talking about the Inverse-Square Relationship for sample size which I introduced in Lesson 1, question 8.
Here is another way to think about the Inverse-Square Relationship. Essentially, if you want your margin of error to get smaller, then you want your
sample size to get larger by the square of the factor. If you want your margin of error to get larger, then you want your sample size to get smaller by the square of the factor.
- This means, if you want to multiply the margin of error, you divide the sample size.
- If you want to divide the margin of error, you multiply the sample
size.
For example, if I want to divide my margin of error by a factor of 7, then I multiply my sample size by a factor of 49 (7-squared). If I want to multiply my margin of error by a factor of 5, then I divide my sample size by a factor of 25 (5-squared).
Don't use the sample size formula in part (d)! It will be too good an answer, possibly. They want you to use the inverse-square
relationship.
If you are having trouble identifying the multiplier they are using in part (d), here is a trick you can use. Divide the larger margin of error by the smaller margin of error as given in parts (a) and (d). That is the factor you want. Then, as always, square it to establish the factor you want to determine your new sample size. Do you want the multiply by that
value, or divide? Do you want the sample size to get larger or smaller?
Make sure you still follow the Paint-Can Principle for your final answer!
Parts (e) and (f) return to just using your sample size formula and making observations about the results.
This is a good run through of confidence intervals and hypothesis testing as I teach in Lesson 8 (see my questions 2 and 3).
Be careful that you don't lose accuracy by rounding off too
much. I suggest you round off to no less than 5 or 6 decimal places while computing things like the standard deviation of p^ to ensure that you get accurate margins of error, and accurate test statistics. Better yet, store exact answers in memory in your calculator.
Part (h) requires an alpha/beta table.
Note that you will need to use the z* critical value you found in part (f)
to compute p^*, the critical value for p^ where you will reject Ho (the p^ decision rule) needed to answer part (g). We derive p^* from the standardizing formula for p^ bell curves.
Question 4: Interpretations
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Part (a): Use the same standard two sentences as always to interpret your confidence interval as I show you way back in Lesson 1, question 1(b). But, keep in mind that you are interpreting a confidence interval for a proportion,
p, not the true mean, mu as I am doing in my example.
Part (b): Follow my examples back in Lesson 2, question 6 to see how to interpret a P-value. As always, first stress that you are assuming Ho is correct (what is Ho in your problem?). Keep in mind that you are testing a hypothesis for two proportions, p1=p2 in your example, not a
mean.
This 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 8.
Be careful that you don't lose
accuracy by rounding off too much. I suggest you round off to no less than 5 or 6 decimal places while computing things like the standard error of p1^-p2^ to ensure that you get accurate z-scores. Better yet, store exact answers in memory in your calculator.
Part (g) introduces the concept I teach in my question 4 in Lesson 9 (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. In other words, you already know the test statistic and P-value. You will be using Table F for the first time in these last two questions. Here is a link where you can
download the table if you have not already done so:
This is standard Two-Way Table Chi-Square analysis as taught in questions 1 through 4 in Lesson 9 of my
book.
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.
- Once you have entered all the info in the cells in the Biology column of your given 2-way table, you then proceed to enter all the info from the Chemistry column of the given 2-way table. Then you enter all the info from the Physics 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.
If you don't get the Contingency Table, you have not properly labeled your data columns! Go back to the top of these steps and check your data columns to make sure they have the correct labels for Data Type and Modeling
Type.
Now upload your output to the HTML Editor:
- If you are using Windows:
- 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 "File" then "Save As" to get a pop-up window.
Type in whatever name you want the file to have in the "File name" section. Click the "Browse Folders" arrow and select which folder you want to save the file in (I suggest you select "Desktop" so that the file will just appear right on your desktop home screen). Finally, click the drop down arrow in the "Save as type" section and select "JPEG File". Click "Save". You should now have your file ready to upload into the assignment.
- To
upload your file into the text box they provide: Click "HTML editor" below the text box (if you have not already done so) to make a toolbar appear in the text box. Click the toolbar option called "Link" and select "Image." In the pop-up window that appears, click the button called "Find/Upload File" (it is at the bottom of the pop-up window, you may have to enlarge the box or scroll down to see it). Click the "Browse" button and find the histogram file you just
saved. Either double-click that file or select it and click "Open" and you should see the path to that file appear in the Browse box. Click "Upload File" and its name should appear in the "Uploaded Files" pop-up window. Select the file in the list of "Uploaded Files" to highlight it and click OK and you should see the file appear in the text box.
- If you are using Apple/Mac:
- You will need to take a screen
shot of your output in order to upload it. To take a screen shot hold down Command+Shift+4 and drag the cross-hairs over the image to capture it. The image will save a .png file to your desktop by default.
- To upload your file into the text box they provide: Click "HTML editor" below the text box (if you have not already done so) to make a toolbar appear in the text box. Click the toolbar option called
"Link" and select "Image." In the pop-up window that appears, click the button called "Find/Upload File" (it is at the bottom of the pop-up window, you may have to enlarge the box or scroll down to see it). Click the "Browse" button and find the histogram file you just saved. Either double-click that file or select it and click "Open" and you should see the path to that file appear in the Browse box. Click "Upload File" and its name should appear in the "Uploaded Files"
pop-up window. Select the file in the list of "Uploaded Files" to highlight it and click OK and you should see the file appear in the text box.
Don't forget to answer their other questions in the HTML editor box!
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.
Make sure you have properly phrased your hypotheses in order to describe the Type I and Type II errors in this problem. They told you this is a test for homogeneity. If these distributions are homogeneous. that would mean that the three courses would have the same grade distributions.
This is standard Two-Way Table Chi-Square analysis as taught in questions 1 through 4 in Lesson 9 of my book. Be sure to put the smaller bound of the P-value in the first box, and the upper bound in the second
box.
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