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AP Statistics - Unit 3 ReviewName: _________________________1. The January 2005 Gallup Youth Survey telephoned a random sample of 1,028 U.S. teens aged 13-17 and asked these teens to name their favorite movie from 2004. Napoleon Dynamite had the highest percentage with 8% of teens ranking it as their favorite movie. Which is true?I. The population of interest is U.S. teens aged 13-17.II. 8% is a statistic and not the actual percentage of all U.S. teens who would rank this as their favorite.III. This sampling design should provide a reasonably accurate estimate of the actual percentage of all U.S. teens who would rank this movie as their favorite.I only B) II only C) III only D) I and II E) I, II, and III___ 2. Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are three high schools in the district, each with grades 9-12. The school board pools all of the students together and randomly samples 250 students. Is this a simple random sample?A) Yes, because the students were chosen at random.B) Yes, because each student is equally likely to be chosen.C) Yes, because they could have chosen any 250 students from throughout the district.D) No, because we can’t guarantee that there are students from each school in the sample.E) No, because we can’t guarantee that there are students from each grade in the sample.___ 3. Placebos are a tool for…A) sampling B) blocking C) blinding D) control E) randomization___ 4. More dogs are being diagnosed with thyroid problems than have been diagnosed in the past. A researcher identified 50 puppies without thyroid problems and kept records of their diets for several years to see if any developed thyroid problems. This is a(n) A) randomized experimentB) surveyC) prospective studyD) retrospective studyE) blocked experiment___ 5. Among a dozen eggs, three are rotten. A cookie recipe calls for two eggs; they’ll be selected randomly from that dozen. Which plan could be used to simulate 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.I only B) II only C) III only D) I or III only E) I, II, or III___ 6. A researcher wants to compare the performance of three types of pain relievers in volunteers suffering from arthritis. Because people of different ages may react differently to medication, 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 level of pain. This experiment…A) is completely randomized B) uses matched pairsC) has two factors, medication and ageD) has one factor (medication) blocked by age E) has one factor (age) blocked by medication type___ 7. The owner of a car dealership planned to develop strategies to increase car sales. He hoped to learn the reasons why many people who visit his car lot do not eventually buy a car from him. For one month he asked his sales staff to keep a list of the names and addresses of everyone who came in to test drive a car. At the end of the month he sent surveys to the people who did not buy a car, asking them why. About one third of the them returned the survey, with 44% of those indicating that they found a lower price elsewhere. Which is true?I. The population of interest is all potential car buyers.II. This survey design suffers from non-response bias.III. Because it comes from a sample, 44% is a parameter, not a statistic.A) I only B) II only C) I and II only D) II and III only E) I, II and III___ 8. Which is true about sampling?I. An attempt to take a census will always result in less bias than sampling.II. Sampling error is usually reduced when the sample size is larger.III. Sampling error is the result of random variations and is always present.A) I only B) II only C) III only D) II and III E) all three___ 9. Which statement about bias is true?I. Bias results from random variation and will always be present.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___ 10. Which is important in designing a good experiment?I. Randomization in assigning subjects to treatments.II. Control of potentially confounding variables.III. Replication of the experiment on a sufficient number of subjects.A) I only B) I and II C) I and III D) II and III E) all three___ 11. To check the effect of cold temperatures on the battery’s ability to start a car, researchers purchased a battery from Sears and one from NAPA. They disabled a car so it would not start, put the car in a warm garage, and installed the Sears battery. They tried to start the car repeatedly, keeping track of the total time that elapsed before the battery could no longer turn the engine over. Then they moved the car outdoors where the temperature was below zero. After the car had chilled there for several hours the researchers installed the NAPA battery and repeated the test. Is this a good experimental design?A) YesB) No, because the car and the batteries were not chosen at random.C) No, because they should have tested other brands of batteries, too.D) No, because they should have tested more temperatures.E) No, because temperature is confounded by brand.___ 12. Twenty dogs and 20 cats were subjects in an experiment to test the effectiveness of a new flea control chemical. Ten of the dogs were randomly assigned to an experimental group that wore a collar containing the chemical, while the others wore a similar collar without the chemical. The same was done with the cats. After 30 days veterinarians were asked to inspect the animals for fleas and evidence of flea bites. This experiment is…A) completely randomized with one factor: the type of collarB) completely randomized with one factor: the species of animalC) randomized block, blocked by speciesD) randomized block, blocked by type of collarE) completely randomized with two factors13. A member of the City Council has proposed a resolution opposing construction of a new state prison there. The council members decide they want to assess public opinion before they vote on this resolution. Listed below are some of the methods that are proposed to sample local residents to determine the level of public support for the resolution. Match each with one of the listed sampling techniques.___ a) Place an announcement in the newspaper asking people to call their council representatives to register their 1. cluster2. convenience4. multistage5. simple (SRS)6. stratified7. systematic8. voluntary responseopinions. Council members will tally the calls they receive.___ b) Have each council member survey 50 friends, neighbors, or co-workers.___ c) Have the Board of Elections assign each voter a number, then select 400 of them using a random number table.___ e) Randomly pick 50 voters from each election district.___ f) Call every 500th person in the phone book.___ g) Randomly pick several city blocks, then randomly pick 10 residents from each block.___ h) Randomly select several city blocks; interview all the adults living on each block.14. Marketing researchers wonder if the color and type of a candy’s packaging may influence sales of the candy. They manufacture test packages for chocolate mints in three colors (white, green, and silver) and three types (box, bag, and roll). Suspecting that sales may depend on a combination of package color and type, the researchers prepare nine different packages, then market them for several weeks in convenience stores in various locations. In this experiment.a. what are the experimental units? ____________________b. how many factors are there? ______c. how many treatments are there? ______d. what is the response variable? ____________________15. Researchers believe that a new drug called Bone Builder will help bones heal after children have broken or fractured a bone. The researchers believe that Bone Builder will work differently on bone breaks than on bone fractures. Bone builder will be used in conjunction with traditional casts. To test the impact of Bone Builder on bone healing, the researchers recruit 18 children with bone breaks and 30 children with bone fractures. Design an appropriate experiment to determine if Bone Builder will help bones heal.16. In response to nutrition concerns raised last year about food served in school cafeterias, the Smallville School District entered into a one-year contract with the Healthy Alternative Meals (HAM) company. Under this contract, the company plans and prepares meals for 2,500 elementary, middle, and high school students, with a focus on good nutrition. The school administration would like to survey the students in the district the estimate the proportion of students who are satisfied with the food under this contract.Two sampling plans for selecting the students to be surveyed are under consideration by the administration. One plan is to take a simple random sample of students in the district and then survey the students. The other plan is to take a stratified random sample of students in the district and then survey those students. a. Describe a simple random sampling procedure that the administrators could use to select 200 students from the 2,500 students in the district.b. If a stratified random sampling procedure is used, give one example of an effective variable on which to stratify this survey. Explain your reasoning.c. Describe one statistical advantage of using a stratified random sample over a simple random sample in the context of this study.17. The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 25% of the pieces show the letter “M”, 10% show the symbol “&”, and the rest just say “Try again”. When you collect a set of three symbols “M”, “&”, and “M” you can turn them in for a free bag of candy. About how many bags will a consumer have to buy to get a free one? Use a simulation to find out.a. Explain how you will use the random numbers listed below to conduct your simulation.b. Carefully label your simulation for 2 trials.c. State your conclusion.18. 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.b. Briefly explain what “not statistically significant” means in this context.c. Briefly explain why the researchers randomly assigned the subjects to the groups.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.e. Briefly explain why the researchers studied only non-smokers.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.Review from Unit 1:19. A machine that fills cans with soda fills according to the Normal model with mean 12.1 oz and standard deviation 0.05 oz. a. If the cans claim to have 12 oz of soda each, what percent of cans are under-filled?b. If a can is found to actually have 12.3 oz of soda, calculate the z-score and interpret the meaning.20. R&D Books reports that they sold an average of 640 books each month with a standard deviation of 320 books. The highest month was reported to have sold 1,120 books. Based on this information, is it reasonable to believe that the distribution of books sold is approximately normal? Explain.Answers1. E2. B3. C4. C5. A6. D7. C8. D9. B10. E11. E12. C13. a. 8b. 2c. 5e. 6f. 7g. 4h. 114. a. candy packagesb. 2 (color of package and type of package)c. 9d. sales of candy15. Block children by either bone fracture or breaks, then randomly assign the children to either cast only or cast and taking Bone Builder. Compare the length of the times it takes for the groups to heal completely.16. a. Assign each student in the district a unique number from 0000 to 2499. Use a calculator or random number table to select 200 numbers. Throw away any repeating numbers. Those students that correspond to the number would be selected.b. Stratify by grade level (elementary, middle, and high school). Students at different levels may have different opinions in food and the value of nutrition. It may also be helpful to compare results between grade levels.c. Using a simple random sample could potentially get all students in one grade level, or none on one grade level (elem, middle, and high). Using a stratified sample would allow the administration to choose students from each grade level in order to represent all levels.17. a. Using two digit numbers, assign 00-24 as games pieces with an M, 25-34 as game pieces with &, and 35-99 as game pieces with Try Again. Using the random number table and looking at the numbers two digits at a time, record below each number the symbol M or &, or an X if they got Try Again. Stop once I have two M's and one &. Count how many numbers there were, which would represent how many bags the consumer would have to buy.b. 69=Try Again, 07=M, 49=Try Again, 19=M, 76= Try Again, 33=&6 bags48=Try Again, 32=&, 47=Try Again, 79=Try Again, 28=&, 31=&, 24=M, 96=Try Again, 47=Try Again, 10=M10 bagsc. My simulation suggests it might take an average of 8 bags to get the M&M symbols. However, it could take up to 10 bags.18. a. Experiment, the drinking of grape juice was imposed on the volunteers.b. That the differences among blood pressure varied the same as it would by chance (or random variation) and not much higher or lower than that.c. In order to equalize the effects of unknown or uncontrollable sources of variation.d. The control group gives them something to compare it to. Maybe people's blood pressure drops or increases at different times of the year, week, etc. e. Blood pressure in smokers could be confounded with the grape juice. We wouldn't know if the change in blood pressure is due to smoking or the grape juice.f. Block the smokers and non-smokers. Then randomly assign half the smokers to drink grape juice and the rest would not drink grape juice. Repeat this process for the non-smokers. Compare the change in blood pressure.19. a. (12 – 12.1) / .05 = -22.3% of the cans are under-filled.b. (12.3 – 12.1) / .05 = 4The z-score is 4. This means this can is 4 standard deviations above the mean.20. (1120 – 640) / 320 = 1.5The z-score of the highest number of books sold is 1.5 According to the normal model, about 6.7% of the data would be above this value. But since this is reported as the highest value, it would mean the data is not approximately normal. ................
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