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Do note that my final exam seminar is the weekend of April 5 and 6. Click here for more details: 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: Did you read my Tips for Assignment 1? If not, here is a link to those important suggestions: Did you read my Tips for Assignment 2? If not, here is a link to those important suggestions: Did you read my Tips for Assignment 3? If not, here is a link to those important suggestions: Did you read my Tips for Assignment 4? 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.
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:
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 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. 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. They don't want to know n,
they want to know what multiplier would be used. For example, if you wanted 7 times the margin of error, then you would invert 7 to 1/7, then square it to 1/7*1/7=1/49=0.0204.. which rounds to 0.020 (three decimal places as they request). Which is to say you would multiply the original sample size by 0.020.
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.
Divide the old margin of error given in part (a) by the new margin of error given in part (d) and square it. That tells you how much to multiply your answer for the sample size in part (a) by. Don't even worry about trying to understand this. 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. This is good practice at the five steps to test a hypothesis. Make sure you have studied Lesson 9 before attempting this question. My question 12 is a similar example.
In part (d) they want you to type the appropriate word in each box
from the two words they suggest. For example, type either less or greater into the first box as appropriate.
Much the same as 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 five steps to test hypotheses again, but you get to skip my step 2. Note that they tell you what to hypothesize about in this part of the question. When they ask for the decision rule, they are asking you to tell them what rule you are using to reject
Ho. In this case, the decision rule is "Reject Ho if the P-value is less than 3%." (Assuming that you are given a 3% level of significance.)
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 |
To use JMP, click "New Data Table", then enter the data into Column 1. Double-click Column 1 and name it Midterm Scores. Now select "Analyze", "Distribution" and highlight "Midterm Scores" 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 "Midterm Scores" 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 inn
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 "Midterm
Scores" 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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