2.6 Is yawning contagious, Part I. An experiment conducted by the MythBusters, a science entertainment TV program on the Discovery Channel, tested if a person can be subconsciously influenced into yawning if another person near them yawns. 50 people were randomly assigned to two groups: 34 to a group where a person near them yawned (treatment) and 16 to a group where there wasn't a person yawning near them (control). The following table shows the results of this experiment. 53 Group Control Treatment Total Yawn 14| 10 Result Not Yawn 24 12 36 Total 34 16 50 A simulation was conducted to understand the distribution of the test statistic under the assump- tion of independence: having someone yawn near another person has no influence on if the other person will yawn. In order to conduct the simulation, a researcher wrote yawn on 14 index cards and not yawn on 36 index cards to indicate whether or not a person yawned. Then he shuffled the cards and dealt them into two groups of size 34 and 16 for treatment and control, respectively. He counted how many participants in each simulated group yawned in an apparent response to a nearby yawning person, and calculated the difference between the simulated proportions of yawn- ing as pertmt, stm - Part,sim- This simulation was repeated 10,000 times using software to obtain 10,000 differences that are due to chance alone. The histogram shows the distribution of the simulated differences. 0.2- 0.1- -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 (a) What are the hypotheses? (b) Calculate the observed difference between the yawning rates under the two scenarios. (c) Estimate the p-value using the figure above and determine the conclusion of the hypothesis test.