**Are All M&Ms Created
Equally? **

**(original by Judy Allard, NBCT,
Vermont) **

Day 1: In this exercise, you are going to use the statistical methods to answer this extremely important question! In addition, you will write up this lab in a "formal" lab report according to the protocol described in the Lab Report Requirements sheet.

__ Before you begin the exercise__, develop a hypothesis
related to the problem question at the beginning of this exercise.
You will have to write a detailed, step-by-step procedure since
the procedure included on this sheet is only a summary.

__Summary of the Procedure__:

Each student group will measure the mass of a sample of 10 M &
M Peanuts of the same color (which have been dipped in milk chocolate
and covered with a thin candy shell) to the nearest hundredth of a
gram. [The first thing you are going to have to do is devised a
method to take an __unbiased__, representative sample from the
population of peanuts you have been given. This method should be
included in your procedure.](__ note data for this part of the lab
is provided __at
http://www.grochbiology.org/StatisticsData.xls)

Express your results in a table. __ ____ Calculate__
the mean, median, mode, variance, standard deviation from the mean
(+/- 1 and +/- 2 deviations) and the standard error (see Statistic
PPT) of the mean for your sample. At the conclusion of
the activity, do the appropriate thing with your population!!! (you
can use Excel to do your calculations).

Express the masses of the peanuts of the class in a frequency distribution table *** and a frequency distribution graph***. These will include all peanuts without regard to color. (Teacher will demonstrate how to do mean, variance, stdev in Excel)

*Class data provided below (link to sample
data).. Using Excel, 0btain the mean and variance from three
other student groups in the class who had different colored peanuts.
Construct a table for this data that includes your own data.
Apply the t test (see Statistics PPT) to compare each of these
populations to your own. Be sure to include all the required
elements of the t test. (*__This part of the lab report,
also in the results section of your lab report, will be completed
after you have received instruction on the t test__*.)
Calculations may be written by hand. Also do a Chi-Square of the
expected colors of skittles versus the actual number counted in
class. (In a bag of Skittles, according to the Skittles website in
2002, the colors were arranged like this; Green: 19.7%, Yellow:
19.5%, Orange: 20.2%, Red: 20%, and Purple: 20.6%.) from
http://wiki.answers.com/Q/What_is_the_percentage_of_each_color_in_a_bag_of_Skittles
and http://www.scientificameriken.com/candy3.asp
)*

Day 2: Design your own labs (work in lab groups)

Question: Working in your groups come up with one difference that can be measured between plain M&M's and Skittles using lab equipment available in the lab.... (standard lab equipment, balances, spectrophotometer, you are only limited by what we own and your imagination). (for example but not limited to: density, volume, light absorbency, solubility...)

__ Write up: (35 points__)

1) Title (include the independent and dependent variables) 1 point

2) Results include:

copy the raw data with all statistics included from day 1 (from Excel): include the hand calculation of standard error of the mean below table (1)

M & M Day 1: " with t-test values (if done by hand include handwritten values) 4 points

M& M Day 1: pick 2 colors and do an evaluation of t-tests (reject null or fail to reject); show calculation of degrees of freedom see Statistics PPT(6 points)

Skittles Day 1: Chi-square of skittle numbers. (2 points) (use provided data: In a bag of Skittles, according to the Skittles website in 2002, the colors were arranged like this; Green: 19.7%, Yellow: 19.5%, Orange: 20.2%, Red: 20%, and Purple: 20.6%.) from http://wiki.answers.com/Q/What_is_the_percentage_of_each_color_in_a_bag_of_Skittles and http://www.scientificameriken.com/candy3.asp ) (skipped this part 2013)

Day1: Graph of all raw M & M data (you may combine into intervals) and generate a normal distribution histogram (4 points)***

1 data table for day 2: (3 points) include a complete title, column heading with any units AND remember to use only horizontal lines between column heading and end of raw data and statistics

3) For Day 2 investigation: your choice of statistical tests (at least 2 types) (2 points)

Day 2: your choice of format for a graphical representation (2 points)

(5 points) Your discussion should include possible explanations of the outcome of these activity based on the t-tests.

Talk about the use of models and samples for understanding populations and statistics.

You can also discuss further areas of research (what would you consider the next step.

State a conclusion that refers to your hypothesis (language!!!) (Recall you cannot PROVE anything only provide support with evidence and no pronouns please).

5) (2 points) References cited (APA) should include the source of your statistical reference tables.

Hints on how to do the distribution graph:

1) paste all the masses in a column

2) Under the
"data" tab pick sort (descending) that will put all the
numbers in order

3) Look at the data and pick
intervals

Example:

Interval (g) # peanuts
Frequency

1.70-1.89
5
.07

1.90-2.09
12
.17

2.10-2.19
17
.24

2.20-2.39
14
.20

2.40-2.59
13
.18

2.60-2.79
4
.06

2.80-2.99
4
.06

3.00-3.19
1
.01

You can do more intervals or less

4) graph using the
"column" pick a vertical alignment

Example Graph....