## Related questions with answers

The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assign ing line positions on voting ballots. Among 4 l different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line. What do the results suggest about how the clerk met the requirement of assigning the line positions using a random method?

Solution

VerifiedResult part (b):

$P(X=40)\approx 0$

Result part (c)

$P(X\geq 41)\approx 0$

When checking for a significant results, you need to include the more extreme causes. Thus for the event of 40 top lines we also need to take into account the case that there are more than 40 top lines (since this is further from the expected value of 20.5 top lines), which is the probability $P(X\geq 41)\approx 0$ in part (c).

Since the probability is very small (less than 0.05), the event of 40 or more top lines is unlikely to occur by chance and thus the result of 40 top lines is significantly high.

Since the 40 top lines is significantly high, this indicates that the clerk did not meet the requirement of assigning the line positions using a random method.

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