Confidence Intervals

Confidence Intervals

A WebQuest for Math 153 (Introduction to Statistical Methods )

Designed by

Donna Hiestand-Tupper
dtupper@ccbcmd.edu

Introduction

In a package of any type of M&M, the M&M Mars company claims there is a certain percentage of each color. For example, in a package of peanut M&M's, 12% are brown, 12% are red, 15% are yellow, 23% are blue, 15% are green and 23% are orange.

In a recently purchased pack of peanut M&M's, 9 of the 65 peanut M&M's were brown. If we were to use this sample to create a 95% confidence interval, we would get an interval (0.055 < p < 0.222).

The Task

Go to the website http://www.global.mms.com/cai/mms/faq.html. On the side of your screen will be information about the proportion of each color plain M&M.

From the M&M web site.

determine the claimed population percentage of each color PLAIN M&M;
buy a package of plain M&M, the package must be larger than a fun-size;
record the total number of each color plain M&M in your package;
determine the percentage of each color plain M&M in your package;
use Statdisk to create a confidence interval for each color plain M&M in your package;
determine the margin of error for each color;
use your TI-83 to create a confidence interval for each color plain M&M in your package;
explain any discrepencies between Statdisk and the TI.

The Process

Record the number of each color M&M in your package.

Brown	Blue	Red	Orange	Yellow	Green	Total

Record the percentage of each color M&M in your package.

% Brown	% Blue	% Red	% Orange	% Yellow	% Green	% Total

Use Statdisk to create a 95% confidence interval for each color plain M&M.

Color	Interval Using Statdisk
Brown	Submit Statdisk printout
Blue	Submit Statdisk printout
Red	Submit Statdisk printout
Orange	Submit Statdisk printout
Yellow	Submit Statdisk printout
Green	Submit Statdisk printout

Use your TI to determine the margin of error and a 95% confidence interval for each color plain M&M.

Color	Formula for Margin of Error	Margin of Error	Interval Using TI
Brown
Blue
Red
Orange
Yellow
Green

Explain any possible discrepencies between Statdisk and the TI;

For each confidence interval, determine if the interval contains the true population proportion of the given color M&M, as determined by the M&M Mars Company.

Color	Interval	Population proportion contained in interval (Yes or No).
Brown
Blue
Red
Orange
Yellow
Green
Orange

Were there any colors that Statdisk would not find the confidence interval for? If so, what was the problem and why did it occur?
Write a brief sentence stating what each confidence interval means. For example, using the introductory example with brown peanut M&M's, "We can say with 95% confidence that the true proportion of brown peanut M&M's in a package is between 0.055 and 0.222 or between 5.5% and 22.2%." Notice that this interval does contain .13 (or 13%), the claim of the M&M Mars Company.

Evaluation

You are required to answer each of the above questions. When grading your web assignment, I will be using the rubric below. Each category (calculation, use of technology, theory and written responses) is worth 25 points. The number of points you get per category is based on the ratings excellent, good, acceptable, poor or blank. Use the rubric below as a self-check before turning in your assignment.

	Excellent 1 (25 Points)	Good 2 (20 Points)	Adequate 3 (15 Points)	Poor 4 (10 Points)	Blank 5 (0 Points)
Calculations	No calculation or roundoff errors are present.	Roundoff errors are present.	Calculation errors present.	Calculation and roundoff errors were made.	No Calculations Shown
Use of Technology	Shows complete and appropriate use of Statdisk & TI.	Shows appropriate use of Statdisk & TI, but a calculation error is present.	Limited or inappropriate use of Statdisk or TI.	No use of Statdisk, but TI-83 was used.	No use of Technology evident.
Theory Comprehension	Shows complete comprehension of the Statistical Theory.	Understands most of the theory, however minor errors made.	Shows some understanding of the theory, however explanations are unclear.	Shows limited understanding of the theory.	No understanding of theory evident.
Written Responses	Well written. Neat, typed. No grammatical or spelling errors.	Ideas clearly presented, but spelling or grammatical errors are present.	Poorly written response. Many spelling or grammatical errors present.	Poorly written response. Many spelling or grammatical errors present. Assignment is hand written.	Questions left blank.

Conclusion

Confidence intervals are a lot like the Range Game on the television game show The Price is Right. On The Price is Right, a person watches a window move until they hit a button to stop it. The contestant stops the window when he/she thinks it contains the price of a prize they are playing for. Every time a person plays the game, the window may or may not contain the true price of the prize. Similarly, confidence intervals give you a range of values that are likely to contain the true population proportion. Every different sample will give you a different confidence interval. However it is important to keep in mind that the population proportion is a fixed number. Either the interval contains the population proportion, or it does not. It is inappropriate to say make a statement to the effect "There is a 95% chance that the true value of the population proportion p will fall between $$ and $$." That statement implies that the population proportion is changing. It is appropriate to make a statement like "We can be 95% confident that the interval from && to && contains the true value of the population proportion p." Remember we are 95% confident that the process will provide an interval that contains the population proportion.

Last updated on August 21, 2005. Based on a template from The WebQuest Page