Using a specially fabricated booth complete with two-way mirror and a hidden camera, the crew of MythBusters set out to see whether a yawn, like a cold, truly can be caught. Their study involved a sample of 50 people. One at a time each person was escorted to go sit in the booth for a period of time. The MythBusters crew decided to use a 2 to 1 randomization plan. As a result about two-thirds (34) of the subjects were ‘seeded’ with a yawn, that is, the person escorting them to the booth purposely yawned just prior to closing the door, while the other 16 subjects were given no yawn ‘seed’. Using the two-way mirror and hidden camera, the crew were able to observe and record the subjects’ yawn status (that is, whether or not the subject yawned). The results are given below:

1. What type of study is described above?

2. The MythBusters crew would like to test the claim those seeded with a yawn will be more likely to yawn using a Z test where p1 = the population proportion of all people who are seeded with a yawn that do yawn, and p2 = the population proportion of all people who are not seeded with a yawn that do yawn. State the hypotheses to be tested in terms of p1 and p2.

3. The MythBusters crew would like to test the claim those seeded with a yawn will be more likely to yawn using a hypothesis test. The denominator of the test statistic is the standard error under H0 which uses the estimate of the common population proportion. Compute an estimate of that common population proportion. Be sure to include the proper symbol, show your work, and provide the value.

4. Clearly explain (and provide numerical support) why we will be unable to complete a hypothesis test using a z test statistic under N(0,1) for this scenario.