Suppose That the Study in Problem #2 Was Performed with a Random

Essay

Suppose that the study in problem #2 was performed with a random sample of $n = 121$ patient contacts where a plain ring was worn, and 40 of these patient contacts resulted in bacterial transmission.
a) Describe the shape, center, and spread of the sampling distribution of $\hat { p }$ if the null hypothesis $H _ { o } : p = 0.25$ were true.






b) Is there convincing evidence that the null hypothesis is not true, or is $\hat { p }$ consistent with what you would expect to see if the null hypothesis were true? Carry out a hypothesis test to answer this question.