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Final Exam Prep Seminar Scheduled
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The Final Exam Seminar will be Friday, December 5 from 9:00 am to 6:00 pm, and will be held on the UM campus (room 100 St. Paul's College).
Did you read my tips on how to study and learn Stat 1000? 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: Confidence Intervals for the Mean and Lesson 9: Hypothesis Testing for the Mean in my book, if you have it, to prepare for this topic. Important
Note: Unlike what I instruct in my book, make sure that you compute a P-value every single time that you perform a hypothesis test. They have decided to not teach about critical values this term, so there is no need to use Table D to get z* or t*, the critical value, for any hypothesis test. Because you are not using critical values, it therefore becomes essential to compute a P-value.
Your steps to test a hypothesis
should always be: - State the Hypotheses and so establish whether the test is upper-tailed, lower-tailed, or two-tailed.
- State the given level of significance, alpha. Let alpha = 5% if none is given.
- Compute the test statistic using the correct formula for z or t.
- Compute the P-value by
marking the test statistic on a bell curve and shading the appropriate region according to your alternative hypothesis.
- State your conclusion knowing that you always reject Ho if the P-value < alpha.
You will be using Table A and Table D while learning Lesson 8 and 9 and doing this assignment. Here is a link where you can download those tables if you have not done so already:
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 can 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? You can download a free sample of my book and audio lectures containing Lesson 1:
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.
This is p-hat bell curve stuff as taught in Lesson 6, question 10 of my book. Very similar to my question 10(c). I recommend you use all the decimal places your calculator shows you (or use the memory button
on your calculator to keep the exact values) while performing your calculations. Once you get your z-score computed, round it off to 2 decimal places as usual. And, make sure you round properly! For example, if z = 2.237 that rounds to 2.24, not 2.23. Look only at the third digit in the decimal to round off to the second decimal place. Of course, Table A will give you four decimal place probabilities as they have requested.
In
p-hat bell curve stuff, you can get inaccurate answers that lead to being marked wrong if you round off inappropriately or round off too much during your calculations.
This is standard sample size stuff, like my questions 6 to 8 in Lesson 8.
Note that part (c) is talking about the Inverse-Square Relationship for sample size which I introduced in Lesson 8, 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. How much have they multiplied or divided the margin of error in part (a) by? Then divide or multiply the sample size you computed in part (a) by the square of that factor. Make sure you still follow the Paint-Can Principle for your
final answer!
This is standard confidence interval for the mean stuff. Also take a look at Lesson 8, question 10 for an example of how to deal with an unusual level of confidence. Note that they want you to put the Lower Limit of the
confidence interval in the first box, and the Upper Limit in the second box.
This is good practice at the four steps to test a hypothesis as I outlined above in the introduction to these tips. Make sure you have studied Lesson 9 before attempting this question. My question 12 is a similar
example. Make sure that you state your hypotheses correctly.
Approach this just like the previous question.
Be sure to read the section in Lesson 8 about "Inferences for the Mean are robust" that I write in the pages leading up to question 1 to understand what they are getting at in part (a) (or remind yourself about the Central Limit
Theorem in Lesson 7). Although we prefer a population to be normal, that is not a necessary condition to test hypotheses or make confidence intervals for the mean. What is important is that we can reasonably assume the distribution of the sample mean is, at least, approximately normal. Can we assume that in this problem? Why or why not?
Again, you are given an unusual level of confidence in part (b) so you will use the technique I
illustrate in Lesson 8, question 10.
Part (c): Look at my Lesson 8, question 1(b) for an example of how to interpret a confidence interval for the mean.
Part (d) is running you through the four steps to test hypotheses again as I outlined above (you get to skip my critical value step). Note that they tell you what to hypothesize about in this part of the
question.
Part (e): Look at my Lesson 9, question 6 for some examples of how to interpret a P-value.
See my steps below to do the JMP for part (f).
Part (g): Make sure you look at my Lesson 9, question 13(d) for an example of the concept of using confidence intervals to test hypotheses.
Confidence Intervals and Hypothesis Tests in JMP
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To use JMP, click "New Data Table", then enter the data into Column 1. Double-click Column 1 and name it Waiting Time. Now select "Analyze", "Distribution" and highlight "Waiting Time" and click "Y, Columns", then
click OK. You are now looking at a histogram and stuff.
To make the confidence interval:
Click the red triangle next to "Waiting Time" then select "Confidence Interval" from the drop-down list. Select "Other" to get a
pop-up menu. Type in the level of confidence you desire as a decimal. For example, if you want a 97% confidence interval, type in 0.97.
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 given at the start of the problem. Click "OK" and JMP gives you the Confidence Interval at the bottom of the printout.
To test the
hypothesis:
Click the red triangle next to "Waiting Time" then select "Test Mean" from the drop-down list. Enter in the mean from your null hypothesis and enter in the given standard deviation . Click "OK" and JMP gives you the hypothesis test at the bottom of the printout. Note that you cannot enter the level of significance they have given. The level of significance is not
relevant to JMP, you will use that yourself to make your decision.
Note that:
Prob > 'z' is the P-value for a two-tailed test.
Prob > z is the P-value for an upper-tailed test.
Prob < z is the P-value for a lower-tailed test
Select the appropriate P-value from this list.
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.
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