“Tongue Piercing May Speed Tooth Loss, Researchers Say” is the headline of an article that appeared in the San Luis Obispo Tribune (June 5, 2002). The article describes a study of 52 young adults with pierced tongues. The researchers believed that it was reasonable to regard this sample as a random sample from the population of all young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 18 of the study participants.
a. Suppose you are interested in learning about the value of p, the proportion of all young adults with pierced tongues who have receding gums. This proportion can be estimated using the sample proportion, ˆ p. What is the value of ˆ p for this sample?
b. Based on what you know about the sampling distribution of ˆ p , is it reasonable to think that this estimate is within 0.05 of the actual value of the population proportion? Explain why or why not.