Stat 1000: Assignment 9 Tips (Distance/Online Sections)

Published: Mon, 03/18/13


 
My tips for Assignment 9 are coming below, but first a couple of announcements.
 
Please note that my final two-day review seminar for Stat 1000 will be on Saturday, Mar. 30 and Sunday, Apr. 7, in room 100 St. Paul's College, from 9 am to 6 pm each day.  This seminar will cover the lessons in Volume 3 of my book.  
 
I am not yet ready to take registrations, but wanted to make sure you were aware of the dates.
 
Did you read my Tips on How to Do Well in this Course? 

Make sure you do:  Tips on How to Do Well in Stat 1000 
 
Did you read my Tips on what kind of calculator you should get?
Tips on what calculator to buy for Statistics
 
Did you miss my Tips for Assignment 8?
Tips for Stat 1000 Distance Assignment 8
 
If you are taking the course by Classroom Lecture (Sections A01, A02, etc.), there is no Assignment 9.
 
Tips for Assignment 9 (Distance/Online Sections D01, D02, D03, etc.)
  
Don't have my book?  You can download a free sample containing Lesson 1 at my website here:
Grant's Tutoring Study Guides (Including Free Samples)
 
Study Lesson 8: Confidence Intervals 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 doing this assignment.  Here is a link where you can download those tables if you have not done so already:
Table A
Table D
 
First, be sure to note whether a question gives you sigma, σ, the population standard deviation, or s, the sample standard deviation.  That dictates whether you will use z or t when making your confidence interval.  I would assume, at this stage, you are likely to be given σ most of the time.
 
Question 1 is using the formula I introduce in question 6 of "The Confidence Intervals for the Mean" lesson.  Make sure you look through my questions 6, 7 and 8 before attempting this question.  Also, take a look at my question 10 for an example of how to deal with an unusual level of confidence.
 
Question 2 is standard stuff.  Note, the margin of error in a confidence interval is everything after the "+/-".  Which is to say, the margin of error is either z* multiplied by the standard deviation of the sample mean, or it is t* multiplied by the standard error of the sample mean.  All confidence interval formulas essentially are "estimate +/- margin of error".
 
Question 3 requires you go to Confidence Interval Applet.  Click the link to go straight to it.
 
To graph your results, use JMP.  Open a "New Data Table" and name your first column something like "Confidence Intervals".  In that column you will type 10, 20, 30, ... 200.  Double-click at the top to the right of your first column to create a second column and name it "Percent Hit" and record the percent hits for your intervals as given by the applet.  You are expecting the Percent Hit to eventually be 95% by the end.  Graph your data as a time series.  Here's how:
To make a Time Series: Select Analyze in the toolbar, then select Modeling in the drop-down list and finally select time series.  Select your time variable ("Confidence Intervals") and click "X, Time ID" and select the other variable you are tracking ("Percent Hit") and click "Y, Time Series".  Click OK.  Just ignore that other pop-up menu asking about time lags or autocorrelations or whatever, click OK and move on.  None of that has anything to do with the time series.
 
Once you have made the time series, use the selection tool (click the blue line or press "Alt" to make the toolbar appear in JMP and click the fat white cross "+" to get the selection tool) to select the time series, copy and paste it into a Word document (or similar word processor), write your comments about what trend you observed, save as a pdf file, and upload to WebAssign.
Personally, I think they should have had you click the "Sample 50" button instead and made you do that several times (say up to a total of 1000 or 2000 confidence intervals).  Try that yourself.  Notice, in the long run, you reach a 95 percent hit rate.  That is because, we know a 95% confidence interval for the population mean, μ, will catch the mean, μ, 95% of the time.  Which is to say, if we make 2000 confidence intervals for the population mean, then we would expect about 95% of them to actually contain the population mean.
 
Again, the trend that should reveal itself in the time series is that, in the long run, you are leveling off at a 95 percent hit rate.
 
Question 4 requires you to copy and paste the data into JMP.  Select and copy the entire data set including the column labels (you could press "Ctrl-A" to select "all" then press "Ctrl-C" to copy it all).  Click "New Data Table", then select "Edit" then "Paste with Column Names".  Now select "Analyze", "Distribution" and highlight "DRP" and click "Y, Columns", then click OK.  You are now looking at a histogram and stuff.  Click the red triangle next to "DRP" then select "Confidence Interval" from the drop-down list.  Select "Other" to get a pop-up menu.  It probably already has 0.95 typed in (for 95% confidence interval), but, if not, be sure to type in 0.95.  Make sure that "two-sided" has been selected and 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.  I believe σ = 11 in your case.  Click "OK" and JMP gives you the Confidence Interval at the bottom of the printout.
 
Now, click the thin blue line at the top of the screen or press "Alt" to get the JMP toolbar.  Select "File," then "Save As."  In the "Save As Type" section, click the arrow to get a drop-down list and select "PDF File".  Click "Save" to save your file then upload it to WebAssign.
 
Question 5 is just more practise at all the stuff I teach in Lesson 8.  Everyone gets different questions here, so I can't be more specific than that.