M&M Statistics
Chi-Square and M&Ms! Have you ever wondered why the package of M&Ms you just bought never seems to have enough of your favorite color? Or, why is it that you always seem to get the package of mostly brown M&Ms? Is the number of the different colors of M&Ms in a package really different from one package to the next, or does the Mars Company do something to insure that each package gets the correct number of each color of M&M? Here’s some information from the M&M website: Color% Per BagBrown13%Blue24%Orange20%Green16%Red13%Yellow14%Today we will determine if the numbers of M&Ms of each color in our packages match the numbers promised by Mars Company within reasonable limits. This will be accomplished through the use of the Chi-Square Test, a statistical tool that determines if differences between our observed measurements (counts of colors from our M&M sample) and our expected (what the Mars Co. claims) are simply due to chance or some other reason (i.e. the Mars company’s sorters aren’t doing a very good job of putting the correct number of M&M’s in each package). Procedure: Please round all calculations to the nearest hundredthRecord a null hypothesis for individual and class data.Wash your hands and your desk - you will be handling food that you may want to munch on later. Dump a bag of M&Ms on a paper towel. DO NOT EAT ANY OF THE M&M’S (for now!) Separate the M&M’s into color categories and count the number of each color you have. Record your counts in your Data Table. Post Class Data.Enjoy your M&Ms. Individual Data:Calculate the “Expected” number of M&Ms for each color category based on your total number of M&Ms and the percentages listed above. Calculate Chi Square by writing the category expected/observed values in equation form as shown, then summing the values.Determine the degrees of freedom.Use the table on your AP Biology Formula Chart to determine … P-valueInterpretationTable TalliesDetermine the number of each color of M&Ms and the total number of M&Ms counted at your lab table.Post for Class Data.Class DataCalculate the “Expected” number of M&Ms for each color category based on the total number of M&Ms and the percentages listed above. Determine Chi Square by writing the category expected/observed values in equation form as shown, then summing the values.Provide the information indicated.Please complete the Chi Square word problems located on the backside of this sheet.Part II – CalculationsYou must show your work to receive full credit.Please round to the nearest hundredthFor each problem, provide …Null hypothesisChi SquareDegrees of freedomP valueInterpretationOne study of grand juries in Alameda County, California compared the demographic characteristics of jurors with the general population to see if jury panels were representative. The results for age are shown below. The investigators wanted to know if the 66 jurors were selected at random from the population of Alameda County. Only persons 21 and over are considered. The county age distribution is known from Public Health Department data. The study was published in the UCLA Law Review. Is there evidence that the grand juries or selected at random: in other words, can the differences between the proportion of individuals of each age group in the population and individuals of each age group selected for juries be considered insignificant/due to random chance or is jury selection age-biased? Perform a Chi Square Analysis to determine the answer. Age GroupCounty Distribution# of Jurors Chosen21 – 4042%541 – 5023%951 – 6016%19Over 6019%33The table below reflects data from a public opinion poll in which a random sample of 600 male voters and 600 female voters were surveyed to determine if there is a gender gap in voting preferences. In other words, is there a significant difference in the proportion of Democrats, Republicans, and Independents among female voters as compared to male voters? Perform a Chi Square analysis to justify your answer. Voting PreferencesGenderRepublicanDemocratIndependentMale26327661Female22532550I. M. Hoppy, a brilliant and inquisitive Bio II AP student, was walking on a sea shore and noticed that a small snail lived on certain types of seaweeds. He decided to investigate whether the snails preferred certain kinds by counting numbers of snails on the different seaweed species. I.M.’s data is shown below. Do snails appear to have a preference? Do a Chi Square analysis to determine the answer.Type of SeaweedFrequency(Number of snails on each kind of seaweed)Serrated Wrack41Bladder Wrack38Egg Wrack26Spiral Wrack33 Due Friday, 12/2 ................
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