Follow:
|
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: Please note that I made major changes to my book in the current edition (September 2014). If you are using a book older than September 2014, you are missing about 100 pages of new material in an entirely new lesson on
Probability.
Study Lessons 1, 2 and 3 in my study book (if you have it) to learn the concepts involved in Assignment 1. 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 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 or audio lectures? You can download a free sample of my book and audio lectures containing Lesson 3:
A Warning about StatsPortal
|
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 Size Determination
|
This is a good overview of the concepts I teach in Lesson 1. Especially look at my questions 6, 7 and 8. Use the Inverse-Square Relationship I introduce in question 8 to answer parts (c) and (d).
Careful, in part
(c), they only want the multiplier. Which is to say, if you want to cut the margin of error to one-quarter the size, 1/4 inverted and squared is 16, so you want to multiply by 16. Just enter 16 in the box.
In part (d), where they don't give you the multiplier, take the old margin of error given in (a), and divide it by the new margin of error in (d) to get the appropriate factor. Now merely square that factor. Take that result and multiply
it by the sample size found in (a) to get the answer you desire. Do not use the sample size formula to answer this question. It is too accurate. They want you to use the inverse-square relationship. Don't forget to round your answer for n properly, using the Paint-Can Principle.
Note that, in part (e), you should just use the sample size formula, just like you did in parts (a) and
(b).
This is a good run-through of errors and power in hypothesis testing as I teach in Lesson 3. Make sure you round off to four decimal places as required. Don't just trim your answers. For example, if you get 1.23456
and you are rounding to four decimal places, you would round that off to 1.2346. They do not make it clear, so I would assume that once you have computed the critical value for x̅ (what I call x̅*), and you have entered it into the relevant box in part (a), use this rounded off value for any future calculations. You may want to clarify with the prof as to whether they expect you to use the rounded off numbers for future calculations in the problem, or if they
want you to use the non-rounded values.
BE CAREFUL! Make sure you are using the correct value for z*. Is the test upper-tailed, lower-tailed, or two-tailed? What does that mean about z*? Keep that in mind for all the problems in this assignment.
Just like question 2 above.
Yet more of the same. To do part (c) more easily, read my part of Lesson 3 talking about "The Relationship between the Alternative Mean and the Power of a Test."
Question 5: Type I and Type II Error
|
This is just a matter of typing your explanations into the box provided. Make sure you click the HTML Editor link below the textbox before you type anything in. This is like what I discuss at the start of Lesson 3 where the Type I error is "saying someone does not
have cancer when they actually do." Note that they also want you to describe the consequences of each error. In my example, the consequences of a Type I error would be someone with cancer has gone undiagnosed, which may seriously affect their health, or perhaps even lead to a premature death.
Question 6: Hypothesis Test - Z or T
|
This is a standard hypothesis test question where they have you do all five steps eventually, as taught in Lesson 2 of my book. Make sure you are following their instructions for rounding off the decimals in each part. The fact that they expect you to give
them an exact value for the P-Value pretty much assures you as to whether this is a z or t problem, although you should be able to tell that from the opening paragraph.
Never forget! If sigma, the population standard deviation is given, then you can use z. If you are not given sigma, you must use t.
Question 7: Hypothesis Test - Acid Rain
|
This should be done both by hand (i.e. just using your calculator) and with JMP.
Click the HTML Editor link below the textbox before you start typing any answers in. To type in the formula you are using and to show your numbers subbed into
the formula click the button in the textbox that looks like the Sigma Summation symbol. Then click the various buttons to make your fractions and enter the symbols. Note, on my computer at least, when I click this Sigma button, the pop-up screen to enter the math equation gets hidden behind my webpage, so I have to minimize the StatsPortal screen in order to see the equation editor window.
Part (a) is fundamental. See my discussion in Lesson 1 on
why Inferences for the Mean are robust. It is not essential that a population be normally distributed. All that matters is whether we can assume the distribution of sample means are approximately normal.
Part (b) is using an unusual level of confidence. See my question 10 in Lesson 1 for an example. Note that they want you to explain how you get z*.
Part (c) is standard. I
show you how to interpret a confidence interval in Lesson 1.
Note that you already know the z* critical value for part (d). You used it in part (b). You can use the Equation Editor as I mentioned above to write the formula work you are doing. By saying "differs from 5.0" in this part, they have made it clear what the hypotheses should be.
Parts (e) and (f) are standard P-value stuff. I show you how
to interpret a P-value in Lesson 2, question 6.
Don't forget to answer part (h) in the text box! I discuss this concept in Lesson 2, question 13(d) of my book.
Part (g): First, enter the data into JMP manually: Click the "New Data Table" icon on the toolbar at top left in the JMP home screen. You are automatically taken to an empty spreadsheet with one column. Double-click
"Column 1" and change its name to pH Level, or right-click "Column 1" and select "Column Info" and type in the name pH Level and click OK.
Now just type in the various pH Level values in the cells using your "Tab" or down arrow button to move to each proceeding cell. You can also hit "Enter" after each piece of data to enter it and move to the next cell.
Once you have entered all the data
down your columns, you are ready to test the hypothesis and make your confidence interval. In the toolbar at the top, select Analyze then select Distribution. In the "Select Columns" part of the pop-up window, click the column you want to analyze pH Level in this case) to highlight it, and click the Y, Columns button. You should see the pH Level column appear in the section to the right of the "Y, Columns" button. Click
OK.
It now opens yet another pop-up window called "Distributions" where a histogram should appear. Your histogram appears sideways.
To get JMP to make confidence intervals and test hypotheses for the mean:
To get a confidence interval, click the red triangle next to variable pH Level directly above the histogram to get a drop-down list and select "Confidence Interval". In the
pop-up window that appears, select "Other" (even if the level of confidence you desire is in the list) and type in the level of confidence you want (in decimal form, so, for example, 97% is 0.97). Make sure "Two-sided" is selected. You are given a value for sigma, the population standard deviation, so click the "Use known Sigma" checkbox. Click OK. You will get another pop-up window where you can type in your known value for sigma. A Confidence Intervals table will
appear in your output screen at the bottom. Your lower and upper limits are shown under "Lower CI" and "Upper CI" in the Mean row. These answers should agree with your computed answers in part (b) above.
To test a hypothesis, click that same red triangle you used to make a confidence interval and select "Test Mean". Type in the value the null hypothesis believes the mean to be and type in the known value of sigma in the box that says "Enter
the True Standard Deviation to do a z-test ...". Click OK. A "Test Mean = Value" table appears in your output where, among other things, JMP gives you the test statistic and three probability values. Those three probabilities are the P-value for the three possible alternative hypotheses. JMP will use a z statistic since you gave it a sigma value. It is up to you to know what the correct alternative hypothesis is, and so whether the test is two-tailed,
upper-tailed, or lower-tailed.
- Prob > 'z' is the two-tailed P-value.
- Prob > z is the upper-tailed P-value.
- Prob < z is the lower-tailed P-value.
JMP's answer for the P-value should agree with what you calculated yourself in part (e). There might be a slight disagreement due to the greater accuracy in JMP, but your P-value should be at least identical to three
decimal places. - 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.
Question 8: Hypothesis Test - Radiation
|
This is basically a repeat of question 7, but now you are using t. Do not use Stat Mode on your calculator to compute the mean and standard deviation. I assume those answers would be more precise and lead to issues in StatsPortal.
They want you to use the values for the sample mean and standard deviation they provided to answer the questions.
Part (a) is standard confidence interval stuff. The rest of the question takes you through the five steps to test a hypothesis.
Note, in part (c) enter the LOWER bound of the P-value in the
first box and the UPPER bound in the second box. For example, if you have established that the P-value is between 0.02 and 0.01 (I am just making those numbers up and have no idea what you will determine), type "0.01" in the first box and "0.02" in the second box.
Note: If you ever get a t test statistic that is off the charts on Table D because it is so small that it is off the left edge, or so large that it is off
the right edge, do this:
- Assume that there is a column labeled 0.50 on the far left of the table, and a column labeled 0 on the far right (since the upper tail areas get steadily smaller as you read from left to right).
- If you have a test statistic that is off the left edge of the table, then the upper tail must be between 0.50 and 0.25 (although get in the habit of listing the smaller one first, so say it is between 0.25 and
0.50).
- If you have a test statistic that is off the right edge of the table, then the upper tail must be between 0.0005 and 0 (again say it is between 0 and 0.0005).
- Don't forget to double these bounds if you are doing a two-tailed test!
For part (e), follow exactly the same JMP steps I outlined in question 7 above to do the JMP in this question. Make a New Data Table, naming the column
Radiation. This time, you do not have a value for sigma, so leave the "Enter the True Standard Deviation ..." box in the Test Mean screen empty.
Again, you are given a choice of three probabilities "Prob > 't'," "Prob > t," and "Prob < t" in the Test Mean = Value part of the output. That gives you the two-tailed, upper-tailed, and lower-tailed P-value, respectively. You should know which of those is appropriate for
the hypothesis test you have been doing. (That exact P-Value better agree with the bounds you established earlier.)
Question 9: Hypothesis Test - Detergent
|
Yet another hypothesis test as I teach in Lesson 2. Thankfully, no JMP required. Very similar to the previous question.
|
|
