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Lab 61: Confidence Intervals on Proportions
In this lab you're going to use the simulation at http://statweb.calpoly.edu/chance/applets/Reeses/ReesesPieces.html to take virtual samples of Reese's pieces (sorry no real chocolate)
Open up the simulator and set π = .3. This is really p, but on my screen it comes out as π, set Sample Size, n = 30 . This means we are setting the proportion of orange Reese's pieces as .3

When you click on "Select Sample" the computer will pull 30 Reese's pieces, and put them in bins as orange, yellow, and dark brown and it will tell you p for orange.
What you're going to do is repeatedly sample, using the simulator, and after each sample calculate confidence intervals for confidence levels of 60%, 80% and 99%. You'll (ok, the computer, will do a total of 20 samples). Then we'll see how many confidence intervals at each level contain the actual population proportion.
Some formulas and items you will need:

CI = p± z*σ, where σ=p(1-p)n Remember that p can be given in the problem or a calculated p.
Use the simulator to find p , then calculate the rest to fill in the table. For this lab, σ= .084
If you calculate the # orange, you can use stat-tests-1propZint on your calculator

Sample # | p orange | # orange = 30p | 60% Confidence Interval z*=.84 | 80% Confidence Interval z*=1.28 | 99% Confidence Interval z*=2.58 | | | | Min | Max | Min | Max | Min | Max | 1 | | | | | | | | | 2 | | | | | | | | | 3 | | | | | | | | | 4 | | | | | | | | | 5 | | | | | | | | | 6 | | | | | | | | | 7 | | | | | | | | | 8 | | | | | | | | | 9 | | | | | | | | | 10 | | | | | | | | |

Now plot the intervals on the grids below. Each grid is for a different confidence level;
Confidence Intervals - 60% | | | | | | |…...

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