A report on dental patients with temporomandibular (jaw) joint dysfunction (TMD) was published in General Dentistry (Jan/Feb. 2004). A random sample of 60 patients was selected for an experimental treatment of TMD. Prior to treatment, the patients filled out a survey on two nonfunctional jaw habits - bruxism (teeth grinding) and teeth clenching - that have been linked to TMD. Of the 60 patients, 3 admitted to bruxism, 11 admitted to teeth clenching, 30 admitted to both habits, and 16 claimed they had neither habit.
a. Describe the qualitative variable of interest in the study. Give the levels (categories) associated with the variable.
b. Construct a one-way table for the sample data.
c. Give the null and alternative hypotheses for testing whether the percentages associated with the admitted habits are the same.
d. Calculate the expected numbers for each cell of the one-way table.
e. Calculate the appropriate test statistic.
f. Give the rejection region for the test at α = .05
g. Give the appropriate conclusion in the words of the problem.
h. Find and interpret a 95% confidence interval for the true proportion of dental patients who admit to both habits.