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Name ________________________ AP Statistics Date _____________ Schwimmer Midterm Review #2 1. 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 20-29 age-group and records their age, gender, and party registration (Democratic, Republican, neither). He also selects an independent simple random sample of 60 women from the 40-49 age-group and records the same information. Of the following, which is the most important observation about Jason’s plan? (1) (2) (3) (4) The plan is well conceived and should serve the intended purpose. His samples are too small. He should have used equal sample sizes. He should have randomly selected the two age groups instead of choosing them nonrandomly. (5) He will be unable to tell whether a difference in party affiliation is related to differences in age or to the difference in gender. 2. 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 (group SB) were injured and that about 15 percent of children who were not wearing a seatbelt (group NSB) were injured. Which of the following statements should not be included in a summary report about this study? (1) (2) (3) (4) (5) 3. Driver behavior may be a potential confounding factor. The child’s location in the car may be a potential confounding factor. This study was not an experiment, and cause-and-effect inferences are not warranted. This study demonstrates clearly that seat belts save children from injury. Concluding that seat belts save children from injury is risky, at least until the study is independently replicated. Which of the following statements is true for two events, each with probability greater than 0? (1) (2) (3) (4) (5) If the events are mutually exclusive, they must be independent. If the events are independent, they must be mutually exclusive. If the events are not mutually exclusive, they must be independent. If the events are not independent, they must be mutually exclusive. If the events are mutually exclusive, they cannot be independent. 4. A fair coin is to be flipped 5 times. The first 4 flips land “heads” up. What is the probability of “heads” on the next (5th) flip of this coin? (1) 1 1 (2) 2 4 5 1 1 (3) 1 2 2 4 1 1 (4) 2 2 (5) 0 5. Which of the following is NOT a characteristic of stratified random sampling? (1) (2) (3) (4) (5) 6. Random sampling is part of the sampling procedure. The population is divided into groups of units that are similar on some characteristic. The strata are based on facts known before the sample is selected. Each individual unit in the population belongs to one and only one of the strata. Every possible subset of the population, of the desired sample size, has an equal chance of being selected. a. A new medication has been developed to treat sleep-onset insomnia (difficulty in falling asleep). Researchers want to compare this drug to a drug that has 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? (1) Have subjects choose which drug they are willing to use, then compare the results. (2) Assign the two drugs to the subjects on the basis of their past sleep history without randomization, then compare the results. (3) Give the new drug to all subjects on the first night. Give the old drug to all subjects on the second night. Compare the results. (4) Randomly assign the subjects to two groups, giving the new drug to one group and no drug to the other group, then compare the results. (5) 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. b. Can you think of a better way to complete a study to obtain the same information as above? Matched pairs pairing each subject with himself. Randomly assign subjects into two groups. Group 1 uses treatment 1 the first night and treatment 2 a week later. Group 2 uses treatment 2 the first night and treatment 1 a week later. Then, compare the results for each patient. 7. A spinner on a full circle can take on any decimal value between 0 and 400. What is the probability that the spinner will land between 175 and 225? (1) (2) (3) (4) (5) 8. 50 400 56 400 175 400 200 400 225 400 0 300 100 200 Records from a random sample of dairy farms for the years 1998-2003 yielded the information below on the number of male and female calves born at various times of the day. Males Females Total Day 129 118 247 Evening 15 18 33 Night 117 116 233 Total 261 252 513 What is the probability that a randomly selected calf was born in the night or was a female? (1) (2) (3) (4) (5) 9. 369 513 485 513 116 513 116 252 116 233 A fast-food establishment has many different products for sale. Suppose that 60% of all customers order a hamburger of some kind, 12% purchase a milkshake, and 5% order both. If a customer is randomly selected, what is the probability that he or she ordered neither a hamburger nor a milkshake? (1) 0.05 (2) 0.28 (3) 0.33 (4) 0.48 (5) 0.60 H M .55 .05 .07 .33 10. A suburban school has 4 classes: freshmen, sophomores, juniors, and seniors. The administration wants to compare the quality and taste of the current company that provides pizza at lunch (A) with another company (B). It is interested in which pizza the students like the most, A or B. The population of the school is 1,000 students with each class having roughly the same number of students. A stratified random sample of 40 students will be chosen to taste the pizza (plain pizza only) with each class having equal representation. (a) Decide exactly how you will label the students in order to select your sample. Since you are going to be using a table of random numbers, think this through first. Obtain an alphabetical list of students. Label the students 000-999. Each subject in the experiment will be represented by 3 digits in a table of random digits. Pull off strings of 3-digit numbers until you have 40 people in your sample (ignore repeats since each 3-digit number represents a person). Since our sample is stratified, you should stop when you get 10 people per class. For example, disregard additional freshmen chosen once you get 10 freshmen. (b) Use Table B, beginning at line 130, to select the first 6 students in the sample. (This can be done in different ways!) 690, 516, 481, 787, 174, 095 (c) Diagram how the following experiment would be set up. i) completely randomized Group 1 Treatment 1 20 students Random 40 students Assignment Group 2 Treatment 2 20 students Compare preference in pizza Treatment 1: Eat pizza from company A and decide if they like it. Treatment 2: Eat pizza from company B and decide if they like it. ii) block design with 2 blocks (lower grades 9 and 10 vs. upper grades 11 and 12) Group 1 10 students Block 1 Random Lower grades Assignment Block 2 Random Upper grades Assignment 40 students Group 2 10 students Group 3 10 students Group 4 10 students Treatment 1 Compare preference Treatment 2 Treatment 1 Compare preference Treatment 2 Treatment 1: Eat pizza from company A and decide if they like it. Treatment 2: Eat pizza from company B and decide if they like it. iii) matched pairs (students acting as their own control) Group 1 Treatment 1 20 students 40 students Random Compare preference Assignment in pizza Group 2 20 students Treatment 2 Treatment 1: Eat pizza from company A on first day, then eat pizza from company B on second day. Treatment 2: Eat pizza from company B on first day, then eat pizza from company A on second day. (d) A decision is made to go with the matched pairs design. Assuming that the experimenters have taken reasonable precautions, describe a lurking variable that could present itself in trying to identify what pizza (A or B) the students prefer. Students may recognize the current company’s pizza (A) and because they are accustomed to eating it, they may confuse that recognition with a preference. (This is not the only possible solution!!)