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 ofn =121patient contacts where a plain ring was worn, and 40 of these patient contactsresulted in bacterial transmission.
a) Describe the shape, center, and spread of the sampling distribution of $\hat{p}$ if the nullhypothesis Hpo : = 0.25 were true.
b) Is there convincing evidence that the null hypothesis is not true, or is $\hat{p}$ consistentwith what you would expect to see if the null hypothesis were true?
Carry out ahypothesis test to answer this question.