AP Statistics - COL: Collecting & Producing Data

A researcher wants to determine if watching TV from five feet or closer damages a person's eyes. The researcher wants to know if this is truth or a myth. (a) How can an observational study be performed? (b) How can an experiment be performed? (c) Which approach is more appropriate here? Explain. (d) If an experimental design was implemented, give an ethical consideration that would cause the researchers to halt the experiment early.

High A1C levels (a test for diabetes) can be reduced by either a low-fat diet or a medication such as metformin. Researchers would like to test the effectiveness of metformin and to note whether the effectiveness, if any, is enhanced by diet. A random sample of adults with high A1C levels, on no special diets, and not on medication, are recruited for a study. (a) Conclusions will apply to what population? (b) Explain how you would design a completely randomized experiment. (c) How might you incorporate blocking and for what purpose? (d) How might blinding be incorporated in this study and for what purpose?

A company efficiency expert believes that employees who eat at least 1,000 calories at breakfast have higher productivity levels at work. She interviews a simple random sample (SRS) of 30 employees who claim to eat under 1,000 calories at breakfast and an SRS of 25 employees who claim to eat over 1,000 calories at breakfast. In each group, she looks up productivity levels on the job. (a) Explain why this is an observational study and not an experiment. (b) Give an example of a possible confounding variable with an explanation in the context of this study. (c) If the employees who eat over 1,000 calories have higher productivity records, is it reasonable to encourage all employees to eat larger breakfasts? Explain. (d) How could the efficiency expert design an experiment to study caloric intake at breakfast with productivity in the workplace?

A pastor expects his parishioners to spend some time each week in Bible study. He randomly selects 30 parishioners from among those coming to church one Sunday and asks each the number of minutes spent reading the Bible during the previous week. Using this data, the pastor's secretary, who once took a college statistics class, calculates the following. \(n = 30\) \(\overline{x} = 31.2\) \(s = 13.2\) Min = 13.5 \(Q_1 = 18.7\) Med = 27 \(Q_3 = 41.2\) Max = 57 The pastor asks the secretary to compute a confidence interval estimate of the mean number of minutes parishioners read the Bible weekly. Comment on this study, including necessary assumptions and how well they are met. (You are not asked to calculate the confidence interval.)

A manufacturer of circuit boards wishes to test which of two soldering irons leads to fewer soldering errors. The workroom consists of eight large tables, and the manufacturer plans to have everyone at a given table use the same soldering iron. On one side of the room are windows with a pretty view, and on one side is the floor manager's desk. (a) Suppose you decide to block using the Scheme A below (one block is white, one gray). How would you use randomization, and what is the purpose of the randomization? (You are not asked to give an actual randomization procedure.) (b) Comment on the strength and weakness of Scheme A as compared to blocking Scheme B (one block is white, one gray).

A high school math department conducts a study to determine whether a classroom with windows leads to higher exam scores than a classroom without any windows. Two algebra classes are scheduled, each with 25 students. It is randomly decided which class will use which classroom. During the year, each teacher administers the same exams. At the end of the academic year, overall exam grades are compared. (a) Identify the response variable, the treatments, and the experimental units. (b) Was randomization properly used? Explain. (c) Was replication properly used? Explain. (d) Teacher is a confounding variable. Explain.

How does the American public now feel about leaving Afghanistan? Two surveys are conducted. The survey in VFW (Veterans of Foreign Wars) magazine asks readers to respond concerning whether or not they support the "retreat from Afghanistan." The survey in the newspaper the Washington Post asks readers to respond concerning whether or not they support the "phased troop redeployment from Afghanistan." (a) Give two examples of bias that may have been introduced given the ways in which the samples were selected. (b) Explain how bias may have been introduced given the ways in which the surveys were worded. Suggest different wording to avoid that bias.

A popular coffee chain has 11,500 stores in the U.S. and 13,500 stores outside the U.S. Each store has approximately 10 full-time employees. Suppose the company would like to survey 250 of its employees about new coffee drinks under consideration. Under discussion are three sampling methods. Method 1: A simple random sample Method 2: Randomly pick 125 of their 115,000 U.S. full-time employees and randomly pick 125 of their 135,000 non-U.S. full-time employees Method 3: Randomly pick 25 of their 25,000 stores and pick all full-time employees at these 25 stores (a) Give a design for carrying out Method 1, and give a disadvantage of using Method 1. (b) What is Method 2 called? What is an advantage of Method 2 in this context? (c) What is Method 3 called? What is an advantage of Method 3 in this context?

A medical insurance adjuster wants to interview a random sample of 50 doctors in a city. Suppose there are 25 hospitals, each with 50 doctors. (a) Describe a procedure for using stratified sampling using the hospitals as strata. (b) Describe a procedure for using cluster sampling using the hospitals as clusters. (c) In this context, give an advantage of using stratified sampling over cluster sampling. (d) In this context, give an advantage of using cluster sampling over stratified sampling.

A reading specialist plans a study to determine if high school students read faster from a physical book or on an iPad. The reading specialist randomly selects 60 high school students for the study. (a) Describe a randomization process and an inference procedure for the study to be conducted with a completely randomized design. (b) Describe a randomization process and an inference procedure for the study to be conducted with a matched pairs design.