Test #4 (Chapter 5)Honor Pledge ______

AP StatisticsName ______

10/28/08Wood/MyersPeriod ______

Test #4 (Chapter 5)Honor Pledge ______

Part I - Multiple Choice (Questions 1-10) – Circle the letter of the answer of your choice.

In a certain community, 20% of cable subscribers also subscribe to the company’s broadband service for Internet connection. You would like to design a simulation to estimate the probability that one of six randomly selected subscribers has the broadband service. Using digits 0 through 9, which of the following assignments would be appropriate to model this situation?

(a)Assign even digits as broadband subscribers and odd digits as cable-only subscribers.

(b)Assign 0 and 1 as broadband subscribers and 2, 3, 4, 5, 6, 7, 8,and 9 as cable-only subscribers.

(c)Assign 0, 1, and 2 as a broadband subscriber and 3, 4, 5, 6, 7, 8, and 9 as a cable-only subscriber.

(d)Assign 1, 2, 3, 4, 5, and 6 as a broadband subscriber and 7, 8, 9, and 0 as a cable-only subscriber.

(e)Assign 0, 1, and 2 as a broadband subscriber; 3, 4, 5, and 6 as a cable-only subscriber; and ignore digits 7, 8, 9 and 0.

2. A cause-and-effect relationship between two variables can best be determined from which of the following?

(a) A survey conducted using a simple random sample of individuals.

(b) A survey conducted using a stratified random sample of individuals.

(d) An observational study where the observational units are chosen randomly.

(e) A controlled experiment where the observational units are chosen randomly.

3. Which of the following is a true statement about experimental design?

(a) Replication is a key component in experimental design. Thus, an experiment needs to be conducted on repeated samples before generalizing results.

(b) Control is a key component in experimental design. Thus a control group that receives a placebo is a requirement for experimentation.

(d) Blocking eliminates the effects of all lurking variables.

(e) The placebo effect is a concern for all experimenters.

4. Which of the following sample designs does not contain a source of bias?

(a) A politician would like to know how her constituents feel about a particular issue. As a result, her office mails questionnaires about the issue to a random sample of adults in her political district.

(b) A company uses the telephone directory to randomly select adults for a telephone survey to gauge their feelings toward items manufactured by the company.

(c) An interviewer selects a random sample of individuals to question about a particular issue. Since some of the individuals are not informed about the issue, the interviewer gives background and his personal view on the issue before their responses.

(d) A news show asks viewers to call a toll-free number to express their opinions about a recent high-publicity trial.

(e) One thousand numbered tickets are sold as a fund-raiser. Five numbers are chosen randomly, and the individuals with the winning ticket numbers each win $10.

5. A drug company wishes to test a new drug. A researcher assembles a group of volunteers and randomly assigns them to one of two groups – one to take the drug and one to take a placebo. In addition, the company wants the experiment to be double-blind. What is the meaning of double-blind in this situation?

(a) The volunteers in both groups are blindfolded when they take the drug or placebo.

(b) The volunteers in both groups do not know whether they are taking the drug or the placebo.

(c) Neither the volunteers nor the drug company executives know which volunteers are taking the drug and which are taking the placebo.

(d) Neither the volunteers nor the experimenters know which volunteers are taking the drug and which are taking the placebo.

(e) As long as the subjects are randomly assigned to the two groups, there is no need to make the experiment double-blind.

6. Since many individuals walk around their homes in their socks, a manufacturer has created a material for socks that is believed to be more resistant to wear than cotton. The manufacturer wishes to test this belief over a period of a month. Given a group of volunteers, which of the following designs will best test this new material’s resistance to wear?

(a)Have the volunteers wear the socks made from the new material for a month, and check the wear on the socks at the end of the month.

(b)Allow half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. Compare the wear on the socks at the end of the month.

(c)Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. Compare the wear on the socks at the end of the month.

(d)Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. At the end of two weeks, the volunteers should change sock types. Compare the wear on the socks at the end of the month.

(e)For each volunteer, randomly choose which foot wears a cotton sock, while the other foot wears a sock made of the new material. Compare the wear on the socks at the end of the month.

7. A university is proposing a new procedure for professors to gain tenure. It intends to randomly sample five professors, five assistant professors, five associate professors, five adjunct professors, and five visiting professors. This is an example of what type of sampling design?

(a) Simple random sample

(b) Stratified random sample

(d) Cluster sample

(e) Convenience sample

8. A simple random sample of size n is selected in such a way that

(a) Each member of the population has an equal chance of being selected.

(b) Each member of the population is given an opportunity to respond to the survey.

(d) The probability of selecting any sample is known to be 1/n.

(e) The sample is guaranteed to represent the entire population.

9. A graduate student is conducting an experiment to determine whether a new activity-based method is better than the traditional lecture of teaching statistics. He found two teachers to help him in his study for one semester. Mr. Dull volunteered to continue teaching with traditional lectures and Ms. Perky agreed to try the new activity-based method. Each teacher planned to teach two sections of approximately forty students each for adequate replication. At the end of the semester, all sections would take the same final exam and their scores would be compared. What is the treatment variable in this study?

(a) Teacher

(b) Section of the Course

(d) Final Exam Score

(e) Student

10. Each person in a simple random sample of 2,000 received a survey, and 317 people returned their surveys. How could nonresponse cause the results of the survey to be biased?

(a)Those who did not respond reduced the sample size, and small samples have more bias than large samples.

(b)Those who did not respond caused a violation of the assumption of independence.

(c)Those who did not respond were indistinguishable from those who did not receive the survey.

(d)Those who did not respond represent a stratum, changing the simple random sample into a stratified random sample.

(e)Those who did respond may differ in some important way from those who did not respond.

Part II – Free Response (Question 11-13) – Show your work and explain your results clearly.

11.Your school will send a delegation of 35 seniors to a student life convention. Two hundred girls and 150 boys are eligible to be chosen. A stratified random sample of 20 girls and 15 boys gives each senior the same chance to be chosen to attend the convention.

(a)Is this a random sample from the school? Explain your answer.

(b)Is this a simple random sample from the school? Explain your answer.

12.At a certain university, students who live in dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question.

Many students believe that the food served in the dining hall needs improvement. Do you think that the quality of food served here needs improvement, even though that would increase the cost of the meal plan?

______Yes______No______No opinion

(a)In this setting, explain how bias may have been introduced based on the way this sample was selected and suggest how the sample could have been selected differently to avoid that bias.

(b)In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias.

13.Researchers who are studying a new shampoo formula plan to compare the condition of hair for people who use the new formula with the condition of hair for people who use the current formula. Twelve volunteers are available to participate in this study. Information on these volunteers (numbered 1 through 12) is shown in the table below.

Volunteer / Gender / Age
1 / Male / 21
2 / Female / 20
3 / Male / 47
4 / Female / 60
5 / Female / 62
6 / Male / 61
7 / Male / 58
8 / Female / 44
9 / Male / 44
10 / Female / 24
11 / Male / 23
12 / Female / 46

(a)These researchers want to conduct an experiment involving the two formulas (new and current) of shampoo. They believe that the condition of hair changes with age but not gender. Because researchers want the size of the blocks in an experiment to be equal to the number of treatments, they will use blocks of size 2 in their experiment. Identify the volunteers (by number) that would be included in each of the six blocks and give the criteria you used to form the blocks.

(b)Other researchers believe that hair condition differs with both age and gender. These researchers will also use blocks of size 2 in their experiment. Identify the volunteers (by number) that would be included in each of the six blocks and give the criteria you used to form the blocks.

(c)The researchers in part (b) decide to select three blocks to receive the new formula and to give the other three blocks the current formula. Is this an appropriate way to assign treatments? If so, describe a method for selecting the three blocks to receive the new formula. If not, describe an appropriate method for assigning treatments.