Ask a research question. Is yawning contagious? Conventional wisdom says yes: When we see someone else yawn, we're prone to let out a yawn ourselves. Has this happened to you or have you noticed it in others? Will data support this claim if we put it to a scientific test?

Design a study and collect data. The folks at MythBusters, a popular television program on the Discovery Channel, investigated this issue by using a hidden camera. Fifty people attending a local flea market were recruited to participate. Subjects were ushered, one at a time, into one of three rooms by co-host Kari. She yawned (planting a yawn "seed") as she ushered subjects into two of the rooms, and for the other room she did not yawn. The researchers decided in advance, with a random mechanism, which subjects went to which room. As time passed, the researchers watched to see which subjects yawned.

The researchers found that 11 of 34 subjects who had been given a yawn seed actually yawned themselves, compared with 3 of 16 subjects who had not been given a yawn seed.

Part A:Calculate the conditional proportion of subjects who yawned in the "yawn seed" group, and then do the same for the control group. Then calculate the difference between these proportions, subtracting in the direction "yawn seed" minus control.

We need to perform a large number of repetitions (say, 1,000 or more) in order to assess whether the MythBusters result is typical or surprising when yawning is not contagious. To do this we will use an applet specifi cally designed for this purpose: the Two Proportions applet.Use this applet to conduct 1,000 repetitions of this simulation: Change the Number of Shuffles fto 1000and press Shuffle. The applet produces a dotplot showing the null distribution for the difference in proportions of yawners between the two groups.

Part B:Is the observed value of the statistic from the MythBusters study (0.136) out in the tail of this null distribution or not so much? In other words, does the observed result appear to be typical or surprising when the null hypothesis (that yawning is not contagious) is true? Include a screen shot of your simulation.