Project 74

For this project, you may make the simplifying assumption that the Plain M&Ms in this data set represent a simple random sample from all the Plain M&Ms in the world. Test the hypothesis that the mean of the masses of all Plain M&Ms in the world equals 0.86 grams. (This number was arrived at by dividing the net mass listed on the package by the number of M&Ms in the package.)

This data set was collected in the summer of 2008. Every M & M candy from three Medium Size bags of M & Ms was measured. One bag was of plain M & Ms, (14.0 oz. or 396.9 g), one bag was of peanut M & Ms (also 14.0 oz. or 396.9 g), and one bag was of peanut butter M & Ms (12.7 oz. or 360 g). As summarized in the table below, the data set has four variables: type, color, diameter, and mass.

The variable *diameter* refers to the shortest distance from side to side at the candy's widest height when it is placed flat on the table with the "m" facing up. Put otherwise, when the candy is placed in that position, imagine taking horizontal cross-sections of the candy. They will be roughly elliptical. The diameter of the candy is the length of the minor axis of the largest such cross-sectional ellipse (which will generally be the cross-section at half the total height). As you might expect, this axis can be somewhat difficult to determine and was no doubt a source of measurement error, but this definition of diameter does correspond fairly well to the way that an M & M fits into a caliper.

Diameters were measured with a General Tools Ultratech Fraction+ Digital Fractional Caliper (claimed accurate up to plus or minus 0.02mm), and masses were measured with a MyWeigh Durascale 50 (claimed accurate up to plus or minus 0.01 g). The candies were measured in the order given in the data set, which although not entirely random was not intentionally systematic in any way (other than by type).

The variables in the data set are as follows:

Name | Units | Description |

type | peanut, peanut butter, or plain | type of M&M |

color | blue, brown, green, orange, red, or yellow | color of the candy |

diameter | millimeters | diameter of the candy |

mass | grams | mass of the candy |

The full data set in csv format is at: