Business Statistics
Lecture Review #23 – Model Formulation
Review questions:
1) What distinguishes a controlled experiment from an observational study? What are the relative advantages and disadvantages of each?
2) In comparative experiments, what characterizes paired data? Independent samples?
3) How do we determine when to analyze means and when to analyze proportions, when analyzing data from a study?
4) When do we use confidence intervals to answer research questions? When do we use hypothesis tests?
Model Formulation Exercises:
In each of the following scenarios, indicate (a) whether this is a controlled experiment or an observational study, (b) whether the study features independent samples or paired data, (c) whether the analysis is of means or of proportions, (d) whether the research question calls for use of a confidence interval or a hypothesis test, and (e) the population(s) to which results can be generalized.
Scenario 1:
The Sirius Cybernetics Corporation is the nation’s leading manufacturer of solar powered flashlights. They wish to test the effectiveness of a proposed new advertising campaign, to make sure that it is successful before spending millions of dollars on a nationwide launch of the campaign. Accordingly, they identify ten test markets of comparable size. They run the campaign in five of the markets (randomly selected), and don’t in the other five. They collect data on the number of units sold in each market. They want to know how much the ad campaign increased sales.
Scenario 2:
Does drinking caffeinated beverages shortly before bedtime really keep people awake? Or is it just a “placebo effect” — people think the caffeine will keep them awake, and therefore they have trouble falling asleep?
Muford Thrildsnickle decides to investigate. He recruits eighty volunteer subjects. Each is given a glass of Coca-cola one hour before bedtime. Muford asks each subject, the following morning, whether s/he had trouble falling asleep. However, Muford has randomly divided the subjects into two groups. Members of one group get real Coca-cola; members of the other group get the decaffeinated version of Coca-cola. (Muford doesn’t tell people which group they are in, of course.)
Scenario 3:
Prospective college student Gracetta Squornshellous wants to know whether Stetson University or Rollins “College” graduates make more money upon graduation. She surveys ten people — an English, mathematics, psychology, education, and art major from each school. For each subject, she obtains data on the starting salary.