ASQ - Statistics Division

### Candy Exercise – Simple Data Analysis – Taken from Fall 2003 Newsletter

Abstract: We came up with a fun-filled exercise for visitors to our booth at the Kansas City AQC. The goal was to demonstrate the power of statistical tools and Statistical Thinking to exhibit hall visitors in a fun, entertaining manner – something that could be later developed as a teacher lesson in the “Virtual Academy’ module of the website. The exercise tried to demonstrate Hypothesis testing, Signal-to-Noise ratios, and basic quality tools while developing the knowledge of a popular brand of candy consisting of several flavors (colors). The two hypotheses being tested were: 1. People like all Runt flavors equally, and 2. Bag fill process (by weight) is stable. After the experiment procedure was carried out, the data was analyzed in Minitab. The Chi-Square test for independence was used to analyze the flavor preference, and a P-value close to 0 was obtained, thus rejecting the hypothesis that candy flavors are the same. This seemed to contradict the candy store owner’s casual observation. For the second hypothesis, ANOVA was used to test differences by box (22 bags per box). In this case the null couldn’t be rejected at an alpha of 0.05. Somebody decided to analyze process variation over time with the caution that the order of candy fill at the factory is unknown. The time series order is the order of booth visitor. I and MR charts were plotted for Bag Weight and bag weight by color, and p-chart of “flavor” distribution stratified by color. The control chart for “average weight per piece” gives some insight that bag fill variation is controlled by the relative frequencies of candy color.

Keywords: Statistical thinking - Hypothesis Testing - Signal-to-noise ratio - P-value - Chi-squared Test - Control charts - I and MR chart - P chart - ANOVA

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