Question: A study will be conducted, involving the population of people aged 15 to 19 in a particular country, to determine whether a relationship exists between the response Y (amount spent in dollars in a week on music downloads) and the predictors W (gender) and X (age in years).
(a) If observations are to be taken from every possible conditional distribution of Y given the two factors, then how many such conditional distributions are there?
(b) Identify the types of each variable involved in the study.
(c) Suppose there are enough funds available to monitor 2000 members of the population. How would you recommend that these resources be allocated among the various combinations of factors?
(d) If a relationship is found between the response and the predictors, can this be claimed to be a cause-effect relationship? Explain why or why not.
(e) Suppose that in addition, it was believed that family income would likely have an effect on Y and that families could be classified into low and high income. Indicate how you would modify the study to take this into account.