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EDRM611: Applied Statistics

Activity for Statistics Lesson 4

There are various ways to flip coins. Some have been shown to be fairer than others. The common alternatives are an up-in-the-air flip, spinning on the table top, and the on-edge procedure used here. These each have their own unique problems. Another procedure, using the pseudo-random number generator on the TI-83, is also subject to any bias the pseudo-random number generator might have. (int(2*rand) or RandInt(0,1,5))

If the coins are equally heavy on both sides, and the edge is perpendicular to the faces, it would be reasonable to expect the long-term proportion of heads to be about 0.5. We can state this as:
Our null hypothesis: H0: p=0.5
The alternative hypothesis: Ha: p[not equal]0.5

  1. Each student places 20 pennies on edge on a flat surface (table).
  2. Bang the table just hard enough to cause all the pennies to fall down.
  3. Count how many pennies fall heads up and record only this value on your recording sheet.
  4. Accumulate your results with the other students in the class by handing in the group's sheet.
Note: it might be easier for a pair of students to repeat this experiment four times without regard to which student actually set the pennies upright each time. This also places smaller demands on the total number of pennies required. Also, you may need to skip coins which were mismanufactured or abused.

Note also: Please do not use any foreign (including Canadian) or pre 1959 (Indian head, wheat-back) pennies. It might be instructive to also compare pre 1982 and post 1982 pennies. In 1982 most of the copper was replaced by zinc, resulting in lighter (and cheaper) pennies. Since 1982 pennies were both (primarily copper and zinc) AND were produced both at Philadephia (plain) and Denver (D) AND both large and small date varieties exist, up to 8 total varieties of pennies may be extant for this date! Some types may be exceedingly rare.

Are these results about what you expected, or are you surprised by the results? Do you think it is likely, by chance alone, to obtain results like these results you observed?

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