Test 5A



Chapter 5 Practice Test AP Statistics

1. What do we call a sample that consists of the entire population?

(a) A stratum (b) A multistage sample (c) A mistake (d) A census

2. A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 150 businesses at random. Of these, 73 return the questionnaire mailed by the committee. The population for this study is

(a) all businesses in the college town. (b) all businesses.

(c) the 150 businesses chosen. (d) the 73 businesses that returned the questionnaire.

3. Which of the following is a method for improving the accuracy of a sample?

(a) Use no more than 3 or 4 words in any question

(b) When possible, avoid the use of human interviewers, relying only on computerized dialing

(c) Use large sample sizes

(d) Use smaller sample sizes

4. We say that the design of a study is biased if which of the following is true?

(a) A racial or sexual preference is suspected (b) Random placebos have been used

(c) Certain outcomes are systematically favored (d) The correlation is greater than 1 or less than –1

5. Control groups are used in experiments in order to . . .

(a) Control the effects of lurking variables such as the placebo effect

(b) Control the subjects of a study so as to insure all participate equally

(c) Guarantee that someone other than the investigators, who have a vested interest in the outcome, control how the experiment is conducted

(d) Achieve a proper and uniform level of randomization

6. Which of the following is a key distinction between well designed experiments and observational studies?

(a) More subjects are available for experiments than for observational studies.

(b) Ethical constraints prevent large-scale observational studies.

(c) Experiments are less costly to conduct than observational studies.

(d) An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot

7. Mrs. Cuppett’s statistics class would like to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman, sophomore, junior, and senior classes to complete the survey. This plan is an…..

a) Cluster (b) Convenience (c) Simple random (d) Stratified random

8. Jason wants to determine how age and gender are related to political party preference in his town. Voter registration lists are stratified by gender and age-group. Jason selects a simple random sample of 50 men from the ages of 20 to 29 and records their age, gender, and party registration (Democratic, Republican, neither). He also selects an independent simple random sample of 60 women from the ages of 40 to 49 and recorded the same information. Of the following, which is the most important thought about Jason’s plan?

a) The plan is well conceived and should serve the intended purpose.

b) His sample sizes are too small.

c) He should have used equal sample sizes

d) He should have randomly selected the age groups.

e) He will be unable to tell whether a difference in party affiliation is related to differences in age or to the difference in gender.

9. A study of existing records of 27,000 automobile accidents involving children in Michigan found that about 10 percent of children who were wearing a seatbelt were injured and about 15 percent of children not wearing seatbelts were injured. Which of the following statements should NOT be included in a summary report about this study?

a) Driver behavior may be a potential confounding factor.

b) The child’s location in the car may be a potential confounding factor.

c) This study was not an experiment, and cause and effect inferences are not warranted.

d) The study demonstrates clearly that seat belts save children from injury.

10. A new medicine has been developed to treat sleep-onset insomnia. Researchers want to compare this to a drug that might have been used in the past by comparing the length of time it takes subjects to fall asleep. Of the following, which is the best method for obtaining this information?

a) Have subjects choose which drug they are willing to use, then compare the results.

b) Assign the two drugs to the subjects on the basis of their past sleep history without randomization, then

compare the results.

c) Give the new drug to all subjects on the first night. Give the old drug to all the subjects on the second night. Compare the results.

d) Randomly assign the subjects to two groups, giving the new drug to one group and the old drug to the other group, then compare the results.

11. A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per 100 milligrams of fruit. Six fruit packs were randomly assigned to each of the three storage times. The treatment, experimental unit, and response are respectively:

(a) A specific storage time, amount of vitamin C, a fruit pack

(b) A fruit pack, amount of vitamin C, a specific storage time

(c) Random assignment, a fruit pack, amount of vitamin C

(d) A specific storage time, a fruit pack, amount of vitamin C

12. A Texas school district wants to compare the effectiveness of a standard AP Statistics curriculum and a new “hands-on” AP Statistics curriculum. Two experienced teachers, Mr. Pryor and Mr. Legacy, each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. The subjects in this experiment are

(a) Mr. Pryor and Mr. Legacy. (b) the two AP Statistics curricula.

(c) the students in the four classes. (d) all students taking AP Statistics in Texas.

13. The Texas experiment described in the previous question

(a) has one factor: the AP Statistics curriculum a student is assigned to.

(b) has two factors: the AP Statistics curriculum and the teacher a student is assigned to.

(c) has two factors: the standard curriculum and one with the hands-on approach.

(d) has three factors: the math curriculum, the teacher, and the class a student is assigned to.

14. We wish to draw a sample of size 5 without replacement from a population of 50 households. Suppose the households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random number table is 11362 35692 96237 90842 46843 62719 64049 17823.

Then the households selected are

(a) households 11 13 36 62 73

(b) households 11 36 23 08 42

(c) households 11 36 23 23 08

(d) households 11 36 23 56 92

15. Which of the following statements is FALSE?

(a) Non-sampling errors are often bigger than the random sampling errors in surveys.

(b) Slight changes in the wording of questions can make a measurable difference in survey results.

(c) People will sometimes answer a question differently for different interviewers.

(d) Sophisticated statistical methods can always correct the results if the population you are sampling from is different from the population of interest, for example, due to undercoverage.

For questions 16-17: The goal of a nutritional study was to compare the caloric intake of adolescents living in the rural areas of the United States with the caloric intake of adolescents living in urban area of the United States. A random sample of ninth-grade students from one high school in a rural area was selected. Another random sample of ninth graders from one high school in an urban area was also selected. Each student in each sample kept records of all the food he or she consumed in one day.

16. Is it reasonable to generalize the findings of this study to all rural and urban ninth-grade students in the United States? Explain.

No, the samples include students from only one rural and one urban high school so it is not reasonable to generalize the findings from these schools to all rural and urban ninth-grade students in the US.

17. Researchers who want to conduct a similar study are debating which of the following two plans to use.

• Plan I: Have each student in the study record all the food he or she consumed in one day. Then the researchers would compute the number of calories of food consumed per kilogram of body weight for each student for that day.

• Plan II: Have each student in the study record all the food he or she consumed over the same 7-day period. Then the researchers would compute the average daily number of calories of food consumed per kilogram of body weight for each student during that 7-day period.

Assuming that the students keep accurate records, which plan, I or II, would better meet the goal of the study? Justify your answer.

Since we are assuming that students keep accurate records, Plan II would do a better job of comparing the daily caloric intake of adolescents living in rural areas with the daily caloric intake of adolescents living in urban areas. Both plans take body weight into account by converting to food consumed per kilogram of body weight. Plam II includes a 7-day period (possibly days in school and days at home on the weekend), and there are differences in the caloric intake among days. It would therefore be better to average over the 7-day period rather than considering only the food consumed in one day, as in Plan I. Plan II would provide a more precise estimate.

For questions 18-20: In search of mosquito repellant that is safer than the ones that are currently on the market, scientists have developed a new compound that is rated less toxic than the current compound, thus making a repellent that contains this new compound safer for humans to use. Scientists also believe that a repellent containing the new compound will be more effective than the ones that contain the current compound. To test the effectiveness of the new compound versus that of the current compound, scientists have randomly selected 100 people from a state.

Up to 100 bins, with an equal number of mosquitoes in each bin, are available for use in the study. After a compound is applied to a participant’s forearm, the participant will insert his or her forearm into a bin for 1 min, and the number of mosquito bites on the arm at the end of that time will be determined.

18. Suppose this study is to be conducted using a completely randomized design. Describe a randomization process for this study.

Each of the 100 selected people will be assigned a unique random number using a random number generator. A list of names and numbers will be created and sorted from smallest to largest by the assigned numbers. The first 50 people on the list will be asked to apply the new compound to their right arm and the other 50 people will be asked to apply the current compound on their right arm. The compounds will be put in identical tubes so neither the participant nor the researcher will know which compound is being applied. (Only the analyst will know this information.) Each person will be randomly assigned to a bin by assigning random numbers to the bins using a random number generator. The first person on the list will be assigned to the bin with the smallest number, the second person to the next smallest number, and so on. After each person insert his or her right arm into the bin for one minute, the number of mosquito bites will be counted. The mean number of mosquito bites will be compared.

19. Suppose this study is to be conducted using a matched-pairs design. Describe a randomization process for this study.

Each person will be randomly assigned a bin as described in questions 18. The researchers will distribute two identical tubes, A and B, to each participant. One tube will contain the new compound and the other the current compound. Neither the researcher nor the participant will know which is which. Each participant will apply one compound to one arm and the other compound to the other arm. The assignment of arms is complete using randomization. A random number will be assigned to each participant. The participants with the 50 smallest assigned numbers will apply tube A to their right arm, the other 50 will aqpply tube B to their right arm. Both arms will be inserted into the assigned bin for one minute at the same time and the number of mosquito bites will be counted. The analyst will compute the difference in number of bites for each person.

20. Which of the designs, the one in part (a) or the one in part (b), is better for testing the effectiveness of the new compound versus that of the current compound? Justify your answer.

The matched-pairs design in question 20 is better because one potential source of variation, person-to-person variability in susceptibility to mosquito bites, is controlled.

21. It is believed that 75% of all apartment dwellers in a large city deadbolt their doors in addition to locking them as

an added precaution against burglary. Describe (in words, and in detail) how you would simulate a SRS of 20

apartment dwellers.

Sample: Let the digits 1, 2, and 3 represent apartment dwellers who deadbolt their doors in addition to locking them, and let the digit 4 represent apartment dwellers who don’t deadbolt their doors. Ignore the other digits. Using a random digit table record the first 20 digits in the range 1-4 and count how many 1-3’s you have to get the proportion of apartment dwellers that deadbolt their doors.

For questions 22-23: Bias is present in each of the following sampling designs. In each case, identify the type of bias involved and state whether you think the sampling frequency obtained is lower or higher than the actual population parameter.

22. A political pollster seeks information about the proportion of American adults that oppose gun controls. He asks a SRS of 1000 American adults: "Do you agree or disagree with the following statement: Americans should preserve their constitutional right to keep and bear arms." A total of 910, or 91%, said "agree" (that is, 910 out of the 1000 oppose gun controls).

BIAS: working of questions

Question is worded to produce a higher response in favor of gun control.

23. A flour company in Minneapolis wants to know what percentage of local households bake at least twice a week. A company representative calls 500 households during the daytime and finds that 50% of them bake at least twice a week.

BIAS: undercoverage

Since people who are home during the day have a higher chance of baking bread this will produce a higher percentage than the population.

For questions 24-25: Turkeys raised commercially for food are often fed the antibiotic salinomycin to prevent infections from spreading among the birds. However, salinomycin can damage the birds' internal organs, especially the pancreas. A researcher believes that a combination of selenium and vitamin E in the birds' diet may prevent injury. He wants to explore the effects of two different dosages of selenium (call them S1, S2) in combination with any of three different dosages of vitamin E (call them E1, E2, E3) added to the turkeys' diets. There are 48 turkeys available for the study. At the end of the study, the birds will be killed and the condition of their pancreas examined with a microscope.

24. What is the experimental unit? What are the factors? How many treatments are needed?

Turkeys dosage of selenium & vit E 6 treatments

25. Draw a diagram of the experiment.

G1: 8 turkeys T: S1, E1

G2: 8 turkeys T: S1, E2

Random G3: 8 turkeys T: S1, E3 Examine pancreas

Allocation G4: 8 turkeys T: S2, E1 & compare

G5: 8 turkeys T: S2, E2

G6: 8 turkeys T: S2, E3

26. A new type of fish food has become available for salmon raised on fish farms. Your task is to design an experiment to compare the weight gain of salmon raised over a six-month period on the new and the old types of food. The salmon you will use for this experiment have already been randomly placed I the eight large tanks in a room that has a considerable temperature gradient. Specifically, tanks on the north side of the room tend to be much colder than those on the south side. The arrangement of tanks is shown in the diagram below.

[pic]

Describe a design for this experiment that takes account of the temperature gradient.

The design of the experiment will be matched pair. Because of the room’s symmetry and location, it is possible to match each tank with another that should have very similar, if not equal temperatures. The matchings are 1 and 4, 5 and 8, 2 and 3, and 6 and 7. From each pair, choose one tank to be fed the new food and one tank to be fed the old food. This choice should be done randomly using a random number table, random number table or a flip of the coin. The administrator of the food should not be aware which tank is getting the new food and which tank is getting the old food. The food should be administered at the same time for all tanks in the same amount.

(You could also draw a chart for this. Make sure you mention why it is a Matched Pair design, all the variables that need to be controlled and how you are doing it, and make it double-blind in the sentences under the chart.)

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