The game of roulette consists of a wheel with 38 colored and numbered slots. The numbers are 1 to 36, 0 and 00. Half of the slots numbered 1 to 36 are red and the other half are black. The two “zeros” are green. The wheel is spun and an iron ball is rolled, which eventually comes to rest in one of the slots. Gamblers can make several different kinds of bets. Most players bet on one or more numbers or on a color (black or red). Here is the layout of the roulette betting table:

Two statisticians recorded the bets on 904 spins. There were 21,731 bets.
Researchers wanted to use these data to examine middle bias, which is the tendency for guessers in multiple-choice exams to select the middle answers. For example, if there are five choices a, b, c, d, and e, guessers will tend to select answer c.
Most players stand on both sides of the betting table so that the middle numbers are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, and 35.
a. If there is no middle bias, what proportion of the bets will be on 1 of the 12 middle numbers?
b. Conduct a test at the 5% significance level to determine whether middle bias exists.
c. The middle of the middle are the numbers 17 and 20. If there is no middle bias, what proportion of the bets will be either 17 or 20?
d. Test with a 5% significance level to determine whether middle of the middle biasexists.

Transcribed Image Text:

0 3 69 12 15 18 21 24 27 30 33 36 00 2 5 8 11 14 17 20 23 26 29 32 35 1 4 7 10 13 16 19 22 25 28 31 34