NAME________KEY___________ DATE: ______________________ AP/ACC Statistics Unit 3 – Review Review 1. What are the two different types of observational studies? Retrospective observational studies (look at data on what has already happened in the past) Prospective observational studies (selecting a sample, then observing what happens to them over a period of time in the future) 2. What are the requirements in experimental design? Control Randomization Replication (Blocking) 3. What must be done in order to make a conclusion about causation? A controlled experiment with statistically significant results 4. Does random assignment eliminate the effects of other variables? No. It may minimize the effects, but it cannot eliminate them. 5. What is the difference between strata and clusters? Strata are chosen so that each stratum is purposefully different from the others in a way that is significant for what is being studied. Clusters are chosen so that each cluster is roughly similar to the others, that way each cluster is (hopefully) representative of the population as a whole. 6. What are the different types of bias? What is the danger of each? Undercoverage—some members of the population have a smaller chance of being selected and these members may differ from those that are selected in a significant way Voluntary response bias—members of the population volunteer themselves to be part of the sample; they may only be taking part if they have a strong opinion they want to be stated Nonresponse bias—no data is collected from some of the people what were randomly selected Response bias—the measurement process itself is biased (leading questions, the wording of the questions, etc.) Convenience sampling—only surveying those that are easy to find (example: Mr. Shaver polling only his AP Stats class for an opinion of all Chaminade seniors) 7. In a simple random sample, which is true: (a) each individual in the population has an equal likelihood of being chosen. (b) each sample of a certain size has an equal likelihood of being chosen. 8. The factors in an experiment are… (select all that apply) (a) the variables being controlled for (b) the variables being blocked for (c) the variables being randomized against 9. What does it mean for the results of a study to not be statistically significant? We can’t justify ruling out the possibility that the differences we have observed are simply due to the chance variation of the random assignment. 10. Sugar Bombs cereal is including a Sherlock Holmes action-figure in each box during a promotion. Claire plans to purchase boxes until she has all five action-figures. How many boxes should she expect to buy if each figure is equally likely to be in any box? (a) Describe how you will use a random number table to conduct this simulation. Let the numbers 0-4 represent each of the five action figures. Take digits from a random number table, ignoring any digits greater than 4. Count the number of digits (0-4) from the table, including repeats, that are needed in order to achieve all 5 numbers. This is one trial. (b) Show three trials by clearly labeling the random number table given below. Specify the outcome of each trial. 73184 95907 05179 51002 (10 boxes) 83374 52297 07769 99792 78365 93487 72753 36216 (15 boxes) 07230 35793 71907 65571 66784 (10 boxes) 25548 91861 15725 (c) State your conclusion. She should expect to buy about 12 boxes on average. 11. Among a dozen eggs, three are rotten. A cookie recipe calls for two eggs; they’ll be selected randomly from that dozen. Which simulation plan could be used to estimate the number of rotten eggs that might be chosen? I. Let 0, 1, and 2 represent the rotten eggs, and 3, 4, …, 11 the good eggs. Generate two random numbers 0-11, ignoring repeats. II. Randomly generate a 0, 1, or 2 to represent the number of rotten eggs you get. III. Since 25% of the eggs are rotten, let 0 = rotten and 1, 2, 3 = good. Generate two random numbers 0-3 and see how may 0’s you get. A) I only B) II only C) III only D) I or III only E) I, II, or III 12. Hoping to get information that would allow them to negotiate new rates with their advertisers, Natural Health magazine phoned a random sample of 600 subscribers. 64% of those polled said they use nutritional supplements. Which is true? I. The population of interest is the people who read this magazine. II. “64%” is not a statistic; it’s the parameter of interest. III. This sampling design should provide the company with a reasonably accurate estimate of the percentage of all subscribers who use supplements. A) I only B) I and II only C) I and III only D) II and III only E) I, II, and III 13. Suppose the state decides to randomly test high school wrestlers for steroid use. There are 16 teams in the league, and each team has 20 wrestlers. State investigators plan to test 32 of these athletes by randomly choosing two wrestlers from each team. Is this a simple random sample? A) Yes, because the wrestlers were chosen at random. B) Yes, because each wrestler is equally likely to be chosen. C) Yes, because stratified samples are a type of simple random sample. D) No, because not all possible groups of 32 wrestlers could have been the sample. E) No, because a random sample of teams was not first chosen. 14. Which statement about bias is true? I. Bias results from random variation and will always be present. No, this is error, not bias. II. Bias results from a sampling method likely to produce samples that do not represent the population. III. Bias is usually reduced when sample size is larger. A) I only B) II only C) III only D) I and III only E) II and III only 15. A researcher identified 100 men over forty who were not exercising and another 100 men over forty with similar medical histories who were exercising regularly. She followed all the men for several years to see if there was any difference between the two groups in the rate of heart attacks. This is a(n) … A) survey B) prospective study C) retrospective study D) randomized experiment E) matched pairs experiment. 16. In an experiment the primary purpose of blinding is to reduce … A) bias. B) confounding. C) randomness. D) undercoverage. E) variation. 17. Does donating blood lower cholesterol levels? 50 volunteers have a cholesterol test, then donate blood, and then have another cholesterol test. Which aspect of experimental design is present? A) randomization B) a control group C) a placebo D) blinding E) none of these 18. A researcher wants to compare the performance of three types of pain relievers in volunteers suffering from arthritis. Because people of different ages may suffer arthritis of varying degrees of severity, the subjects are split into two groups: under 60 and over 60. Subjects in each group are randomly assigned to take one of the medications. Twenty minutes later they rate their levels of pain. This experiment … A) is completely randomized. B) uses matched pairs. C) has two factors, medication and age. D) has one factor (medication) blocked by age. E) has one factor (age) blocked by medication type. 19. A polling organization is investigating public opinion about cloning. They phone a random sample of 1200 adults, asking each person one of these questions (randomly chosen): A: “Do you favor allowing doctors to use cloned cells in attempts to find cures for such terrible diseases as Alzheimer’s, diabetes, and Parkinson’s?” B: “Should research scientists be allowed to use cloned human embryos in their experiments?” Which question do you expect will elicit greater support for cloning? Explain. What kind of bias is this? Question A will be biased toward “yes” because of the words “for such terrible diseases as …” This is an example of response bias (leading questions) 20. A headline in the New York Times announced “Research shows running can alter one’s moods”. The article reported that researchers gave a Personality Assessment Test to 231 males who run at least 20 miles a week, and found “statistically significant personality differences between the runners and the male population as a whole.” Do you think the headline was appropriate? Explain. No, since this is an observational study and not an experiment. There are likely to be other variables (like having the free time to run 20 miles a week) that may actually be causing the mood difference rather than running. We can’t know without an experiment with a control group. 21. Administrators of the fire department are concerned about the possibility of implementing a new property tax to raise moneys needed to replace old equipment. They decide to check on public opinion by having a random sample of the city’s population. a. Several plans for choosing the sample are proposed. Write the letter corresponding to the sampling strategy in the blank next to each plan. __B__i. The city has five property classifications: single family homes, apartments, condominiums, A. convenience temporary housing (hotel and campgrounds), and retail property. Randomly select ten residents from B. stratified each category. C. simple __C__ii. Each property owner has a 5-digit ID number. Use a random number table to choose forty D. cluster numbers. E. systematic __E__iii. At the start of each week, survey every tenth person who arrives at the city park. __D__iv. Randomly select 20 city blocks and survey all the residents in each block. __A__v. Have each firefighter survey 10 of his/her neighbors. b. Name and briefly describe the kind of bias that might be present if the administration decides that instead of selecting people randomly they’ll just… i. interview people about the new property tax at a fire station open house. Undercoverage—those at the open house are likely those in support of the fire department; those not in support are probably not represented. This is biased toward supporting the new tax. ii. ask people who are willing to be taxed to sign a petition. Response bias—the measuring process is systematically biased toward the response the surveyors are seeking. 22. Researchers who wanted to see if drinking grape juice could help people lower their blood pressure got 120 non-smokers to volunteer for a study. They measured each person’s blood pressure and then randomly divided the subjects into two groups. One group drank a glass of grape juice every day while the other did not. After sixty days the researchers measured everyone’s blood pressure again. They reported that differences in changes in blood pressure between the groups were not statistically significant. a. Was this an experiment or an observational study? Explain briefly. An experiment since researchers intervened, setting up a control group and using random assignment. b. Briefly explain what “not statistically significant” means in this context. The reduction in blood pressures is not large enough. We cannot justify ruling out the possibility that the differences in changes in blood pressure are due only to the chance variation in the random assignment. In other words, the reduction in blood pressure can likely be attributed to the chance variation in random assignment. c. Briefly explain why the researchers randomly assigned the subjects to the groups. Random assignment allows them to minimize the effects of unknown or uncontrollable sources of variation, making two groups that are nearly equal. d. Since everyone’s blood pressure was measured at the beginning and at the end of the study, the researchers could have simply looked at the grape juice drinkers to see if their blood pressure changed. Briefly explain why the researchers bothered to include the control group. The control group provided a basis for comparison after the sixty days to determine if the group drinking grape juice had lower blood pressure because of the juice. Maybe everyone’s blood pressure naturally drops at a certain time of the year. e. Briefly explain why the researchers studied only non-smokers. By studying only non-smokers the researchers were trying to reduce any impact the smoking might have had on blood pressure. The researchers were trying to remove any confounding the smoking might have made on blood pressure. f. Other researchers now plan to replicate this study using both smokers and non-smokers. Briefly describe the design strategy you think they should use. Block by smoking status, randomly assigning people in each block to the treatments. Compare blood pressure after 60 days within each block.
