Assignment 3: The Case of Ms. Williams (boys vs. girls)

The case of Ms. Williams (thinks she is biologically wired to have only boys because she had 3 boys in a row)

• We did a random number generation on a TI-86 calculator, using only the numbers 0 and 1, assuming that 1s were boys:

0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1

• EXACTLY three boys in succession occurs four times (in bold and underlined)
• The event “exactly three boys in succession” is likely to occur…
  • 4 / (100-2) = .04
• MORE than three boys in succession occurs six times (in italics and underlined)
• The event “more than three boys in succession” is likely to occur…
  • 6 / (100-2) = .06
• The proportion of boys vs. girls in the sample of 100:
  • 61/100 = .61 (boys)
  • 39/100 = .39 (girls)

• If the coin was flipped 10,000 times, rather than 100 times, the proportion of boys would be a lot closer to .50. This is because although each individual coin toss is random, it is just as likely for it to be a head as it is a tail.

References:

TI-86 Calculator

(Done by Carolyn & Kate)

Advertisement