Statistics Free Response Question Form B

Statistics Free Response Question Form B 2. People with acrophobia (fear of heights) sometimes enroll in therapy sessions to help them overcome this fear. Typically, seven or eight therapy sessions are needed before improvement is noticed. A study was conducted to determine whether the drug D-cycloserine, used in combination with fewer therapy sessions, would help people with acrophobia overcome this fear. Each of 27 people who participated in the study received a pill before each of the two therapy sessions. Seventeen of the 27 people were randomly assigned to receive a D-cycloserine pill, and the remaining 10 people received a placebo. After the two therapy sessions, none of the 27 people received additional pills or therapy. Three months after the administration of the pills and the two therapy sessions, each of the 27 people was evaluated to see if he or she had improved. a) Was this study an experiment or an observational study? Provide an explanation to support your answer. This study was an experiment because people with acrophobia were given 2 different treatments, D-cycloserine or placebo, by the people conducting the study. b) When the data were analyzed, the D-cycloserine group showed statistically significantly more improvement than the placebo group did. Based on this result, would the researchers be justified in concluding that the D-cycloserine pill and two therapy sessions are as beneficial as eight therapy sessions without the pill? Justify your answer. It cannot be justified those 2 different therapy sessions with the d-cycloserine is as beneficial as 8 therapy sessions with no pill. In the experiment, the two-variable studied were 2 sessions with the pill or with the placebo. The variable 8 therapy sessions with no pill were not tested, and therefore cannot be compared to the data collected. c) A newspaper article that summarized the results of this study did not explain how it was determined which people received D-cycloserine and which received the placebo. Suppose the researchers allowed the therapists to choose which received D-cycloserine and which received the placebo, and no randomization was used. Explain why such a method of assignment might lead to an incorrect conclusion. This may lead to an incorrect conclusion as it introduces bias into the study. Researchers assigning the treatments not randomly may add confounding variables which could skew the results (Some confounding variables can be severity, gender). If the therapists know who receives the treatment, they may act differently to one group which can bias the results. 3. An airline claims that there is a 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets. a) What is the probability that Sam’s first upgrade will occur after the third flight? 0.729 b) What is the probability that Sam will be upgraded exactly 2 times in his next 20 flights? 0.285 c) Sam will take 104 flights next year. Would you be surprised if Sam received more than 20 upgrades to first class during the year? Justify your answer. Given the facts that the probability of getting more than 20 upgrades assuming Sam has a 10% chance each flight is 0.003, which is rather small (<0.05), I would be surprised if Sam receives more than 20 upgrades.