A group of researchers investigated the contamination of medical personnel clothing at a New York hospital since there is a potential for patient exposure to potentially dangerous bacteria. They sampled neckties worn by physicians, physician assistants, and medical students at a teaching hospital in New York. Nearly half (47.6%) of the neckties tested harbored microorganisms that can cause illness. By comparison, only one of the 10 ties worn by security guards tested positive for a disease-carrying microorganism. The researchers want to determine if the difference is statistically significant. Which of the following is an appropriate statement of the null hypothesis?
a. The proportion of contaminated ties from medical personnel is the same as the proportion of contaminated ties from security guards.
b. The proportion of contaminated ties from medical personnel is not the same as the proportion of contaminated ties from security guards.
c. The proportion of contaminated ties from medical personnel is greater than the proportion of contaminated ties from security guards.