Name that Scenario - Below are a number of research problems. For each, first determined and state if the appropriate method to address the problem would be to make a confidence interval (CI) or to conduct a test of hypotheses (HT). Next, if a CI, then provide the notation for the corresponding parameter the CI is for; of if a HT, then clearly state the appropriate null and alternative hypotheses to be tested.

a. A yoga instructor is working on a project in which some high school (HS) students participated in a yoga course during their last semester in HS. The length of time (minutes) that a student could correctly hold a certain yoga pose was collected at the start of the course and then at the end. The instructor wanted to learn if their yoga skills for this pose improved on average (where improvement implies they could hold the correct pose longer and improvement was measured as Time at End less Time at Start.)

b. Researchers want to know what proportion of a certain type of tree growing in a national forest suffers from a disease. They take a representative sample of 200 of the trees from around the forest, test them, and find that 15 of them have the disease

c. Researcher Jessie is studying how the fear of going to the dentist affects the actual number of visits made to the dentist for adults. She asks a random sample of adults whether or not they fear going to the dentist and also how many times they have gone in the past 10 years. She would like to assess if the average number of visits made by adults who fear going to the dentist is higher than the average number of visits for those who don't have that fear