SCCC 312A – ProSeminar in Statistics

Lecture Homework #1

Due Date: 1/16/04 (Friday)

Part I. One purpose of the State Lottery is to generate funds for the State to use in funding public education and providing scholarships to meritorious students. Its continued success depends on the participation of residents of the State of South Carolina. At the same time, there is the feeling that the Lottery leads to unfair taxation of the poor people of the State because they are more prone to play the Lottery because of its “promise of sudden and easy wealth.” Therefore, a researcher would like to determine the percentage of all South Carolina residents of voting age who play the State Lottery (with “play” meaning that the individual has purchased a lottery ticket at least once for the past year). In addition, he is also interested in determining if there is any relationship between playing the Lottery and the age and income level of the individual. Ideally, he would like to ask each and every South Carolina resident of voting age the following questions:

Question 1: Did you purchase a lottery ticket at least once for the past year? Please answer YES or NO.

Question 2: Approximately how much money did you spend purchasing Lottery tickets last year?

Question 3: What is your current age (in years)?

Question 4: Classify your annual income last year according to the following categories: Low (below $20,000); Medium (between $20,001 and $50,000), and High (above $50,001).

These four questions define the following three variables:

PLAY: whether the individual played the Lottery.

AMOUNT: the amount spent in purchasing Lottery tickets.

AGE: age of the individual.

INCOME: income level of individual.

Answer the following questions.

a) What is the population of interest in this study?

b) Classify each of the four variables into whether they are qualitative or quantitative.

c) What is the primary parameter of interest to the researcher?

d) Describe a possible parameter that could potentially measure the relationship between playing the lottery and the income level of the individual.

e) Considering possible time and resource constraints, would it be advisable for the researcher to ask each and every South Carolina voter the three questions above? If no, explain why. If yes, would you personally be willing to do it?

f) Since most logically the answer to question (e) is no, if you could only pose the three questions above to 1000 of these South Carolina voters, how would you choose these 1000 voters? What considerations do you need to take into account in order that the conclusions you will get from your study can be generalized to the whole population?

Part II: Describe a problem that is of interest in your field of study or that is of personal interest to you (could be related to our hobby for instance). Explain why you are particularly interested in this problem. In trying to answer this problem, would you need to gather data? For your situation, describe your

a) Population of interest. Be specific on what units will constitute your population.

b) Describe at least two variables that you will be interested in observing or measuring, and classify whether your variable is quantitative or qualitative.

c) Describe how you will measure or determine the values of your variables. Is it through an experiment, a survey, or an interview?

d) Describe a parameter that will be of interest to you in order to answer your problem.

e) Would it be practical for you to observe every unit of the population? Explain your answer.

f) Since most probably it will not be practical to measure each and every unit in your population, describe how would generate your sample units to measure or observe?

Part III: Problems from the textbook.

On pages 7-8 do: 4, 5, 8

On pages 14-15 do: 17, 19, 23

On page 16 do: 26

On page 21 do: 40, 43

On page 47 do: 47