Stat 1000: Tips for Assignment 9
Published: Fri, 11/04/11
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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:
First, be sure
to note whether a question gives you 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 "+/-".
Question 3 requires you go to http://bcs.whfreeman.com/ips6e/
and click the "Statistical Applets" button and then
click "Confidence Interval". 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.
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 mean μ will
catch μ 95% of the time. Which is to say, if we make 2000 confidence
intervals for μ, then we would expect about 95% of them to actually
contain μ.
Question 4 requires you to copy and paste the data into
JMP. Again, 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 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. You can now select, copy and paste your output to a file ready for upload as usual.
Question 5 is just more practise at all the stuff I teach in Lesson 8.