A smulation was conducted to understand the dstribution of the test statistic un

Question

A smulation was conducted to understand the dstribution of the test statistic under the assumption of independence having someone yawn near another person has no nfluence 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 Pito r.This simulation distribution of the simulated differences Pari,m This simulation was repeated 10,000 times using software to obtain 10,000 differences that are d 02 0.6-040200 2 04 06

Explanation / Answer

1. hypotheses for testing if yawning is contagious, i.e. whether it is more likely for someone to yawn if they see someone else yawning

Ho: Yawning is independent of seeing someone else yawn (Yawning is not contagious)

Ha: Yawning is not indpendent of seeing someone else yawn (Yawning is contagious)

2. observed difference between the yawning rates under the two scenarios.

Control Yawning Rate = 4/16 = .25

Treatment Yawning Rate = 10/34 = .29

There is a differnce of .04 or 4% between the treatment and control groups’ yawning rates.

3. When running the Chi-Square test for independence we get a p-value of 1 > .05, so we fail to reject the null hypothesis and do not have enough evidence to say yawning is contagious.

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