Use the following to answer questions 1 and 2:

Transcription

1 Ch. 5 Review (Part I) Use the following to answer questions 1 and 2: IB Math Analysis A television station is interested in predicting whether voters in its viewing area are in favor of federal funding for abortions. It asks its viewers to phone in and indicate whether they support/are in favor of or are opposed to this policy. Of the 1845 viewers who phoned in, 1499 (81.25%) were opposed to federal funding for abortions. 1. Referring to the information above, the viewers who phoned in are a A) probability sample. D) population. B) simple random sample. E) convenience sample. C) voluntary response sample. 2. Referring to the information above, the sample obtained is A) a simple random sample. B) a single-stage sample. C) a census. D) close to the actual proportion of the population who support/oppose federal funding for abortions. E) probably biased. 3. In order to assess the opinion of students at the University of Michigan on campus snow removal, a reporter for the student newspaper interviews the first 15 students she meets who are willing to express their opinion. The method of sampling used is A) convenience sampling. D) simple random sampling. B) numerical sampling. E) a census. C) voluntary response. Use the following to answer questions 4 and 5: Choose a simple random sample of size three from the following movie titles: 1. Batman Begins 4. The Karate Kid 7. Rocky 2. Casino 5. Superbad 8. Tommy Boy 3. District 9 6. Rambo 9. X-Men Use the numerical labels attached to the names above and the list of random digits below. Read the list of random digits from left to right, starting at the beginning of the list

2 4. Referring to the given information, the simple random sample is A) 565. B) The Karate Kid, Superbad, X-Men. C) Batman Begins, Casino, District 9. D) Superbad, Rambo, Rocky. E) Superbad, Rambo, then Superbad again. 5. If we used another list of random digits to select the sample, which of the following statements would be true? A) We would get the same result that we obtained with the list used here. B) We would get the same movies as those obtained from the sample listed here. C) We would get at most one movie in common with the sample obtained here. D) We would get a completely different sample than that obtained with the list used here. E) It would be just as likely that the sample that we obtained here would be selected as any other set of three movies. 6. A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men s clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. The population of interest is A) the people who respond to the questionnaire. B) all residential addresses in Laramie, Wyoming. C) the members of the marketing firm that actually conducted the survey. D) the 100 addresses to which the survey was mailed. E) all adult men in Laramie, Wyoming.

3 7. The six people listed below are enrolled in a statistics course. Use the list of random digits starting at the beginning of the list, to choose an SRS of size three to be interviewed in detail about the quality of the course. Use the labels attached to the six names. 1. Aaron 4. Price 2. Dylan 5. Savannah 3. Preston 6. Terence The sample you obtain is A) Aaron, Dylan, Price. B) Dylan, Aaron, Savannah. C) Preston, Terence, Savannah. D) any set of three names, but we must exclude Price. E) 2, 7, In order to assess the opinion of students at the University of Montana on campus snow removal, a reporter for the student newspaper interviews the first 15 students he meets who are willing to express their opinion. In this case, the sample is A) all students at the University of Montana. B) the 15 students interviewed. C) all students at universities receiving substantial snow. D) the students attending school during the semester. E) all those students favoring prompt snow removal. 9. A small college has 500 male and 400 female undergraduates. An SRS of 50 of the male undergraduates is selected, and, separately, an SRS of 40 of the female undergraduates is selected. The two samples are combined to give an overall sample of 90 students. The overall sample is A) a stratified random sample. D) a convenience sample. B) a multistage sample. E) none of these. C) a simple random sample.

4 10. In order to select a sample of undergraduate students in the United States, I select an SRS of four states. From each of these states, I select an SRS of two colleges or universities. Finally, from each of these eight colleges or universities, I select an SRS of 30 undergraduates. My final sample consists of 240 undergraduates. This is A) simple random sampling. D) convenience sampling. B) stratified random sampling. E) multistage sampling. C) systematic random sampling. 11. An SRS of 1500 adult Americans is selected, and each person is asked the following question: In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance? Only 29% of those responding answered yes. This survey A) probably understates the percentage of people that favor a system of national health insurance. B) probably overstates the percentage of people that favor a system of national health insurance. C) is reasonably accurate since it used a large SRS. D) is very inaccurate, but neither understates nor overstates the percentage of people that favor a system of national health insurance. Since simple random sampling was used, it is unbiased. E) needs to be larger since only about 30 people were drawn from each state. 12. A 1992 Roper poll found that 22% of Americans say that the Holocaust may not have happened. The actual question asked in the poll was: Does it seem possible or impossible to you that the Nazi extermination of the Jews never happened? Twenty-two percent responded possible. The results of this poll cannot be trusted because A) undercoverage is present. Obviously, people who did not survive the Holocaust could not be in the poll. B) the question is worded in a confusing manner. C) we do not know who conducted the poll or who paid for the results. D) nonresponse is present. Many people will refuse to participate and those that do will be biased in their opinions. E) we don t know if the respondents were randomly selected.

5 13. A call-in poll conducted by USA Today concluded that Americans love Donald Trump. USA Today later reported that 5640 of the 7800 calls for the poll came from the offices owned by one man, Cincinnati financier Carl Lindner, who is a friend of Donald Trump. The results of this poll are probably A) surprising, but reliable since it was conducted by a nationally recognized organization. B) biased, but only slightly since the sample size was quite large. C) unbiased because the calls were randomly made at varying times. D) biased, overstating the popularity of Donald Trump. E) biased, understating the popularity of Donald Trump. 14. A news release for a diet products company reports: There s good news for the 65 million Americans currently on a diet. Its study showed that people who lose weight can keep it off. The sample was 20 graduates of the company s program who endorse it in commercials. The results of the sample are probably A) biased, overstating the effectiveness of the diet. B) biased, understating the effectiveness of the diet. C) unbiased because all 20 people lost weight. D) biased, but they could be more accurate. A larger sample size should be used. E) unbiased since these are nationally recognized individuals. 15. A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men s clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. The chance that all 100 homes in a particular neighborhood in Laramie end up being the sample of residential addresses selected is A) the same as for any other set of 100 residential addresses. B) exactly 0. Simple random samples will spread out the addresses selected. C) reasonably large due to the cluster effect. D) 100 divided by the size of the population of Laramie. E) large since the population of Laramie is small.

6 16. A recent poll conducted by the student newspaper asked, Who do you believe will win the Mississippi State Undergraduate Student Government elections? In order to vote, one had to access the student newspaper s Web site and record one s vote at the student newspaper s Web page. The results of the poll were summarized in a graphic similar to the one below. Total Votes: 24 Based on this information, A) the results of the survey are likely to be reliable since it was an online pole. B) the results of the survey are perfectly reliable since an SRS was used. C) Patel and Patel have such a large majority that, even though there are flaws in the poll, they are still almost certain to win. D) Patel and Patel should win because Mississippi State University has a large student population. E) the results of the survey are likely to be unreliable since the sample size was very small. 17. The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. At both schools a simple random sample of about 3% of the undergraduates is taken. We conclude that A) the sample from Johns Hopkins is more accurate than the sample from Ohio State. B) the sample from Ohio State University is about 20 times more accurate than the sample from John Hopkins University. C) the sample from Johns Hopkins has the same accuracy as the sample from Ohio State. D) it is impossible to make any statements about the accuracies of the two samples since the students surveyed were different. E) the sample from Johns Hopkins is less accurate than the sample from Ohio State.

7 18. A sociologist wants to study the attitudes of American male college students toward marriage and husband and wife relations. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. All 25 complete and return the questionnaire. The population of interest in this situation is A) all men taking a comparable sociology class. B) all American male college students. C) all the men in the Sociology 101 class. D) all married men in the Sociology 101 class. E) the 25 men who received and returned the questionnaire. 19. A researcher is interested in the cholesterol levels of adults in the city in which she lives. A free cholesterol screening program is set up in the downtown area during the lunch hour. Individuals can walk in and have their cholesterol levels determined for free. One hundred and seventy three people use the service, and their average cholesterol level is The sample obtained is an example of A) a simple random sample, since the experimenter did not know beforehand which individuals would come to the screening. B) a non-biased survey. C) a stratified sample of high and low cholesterol individuals. D) a sample probably containing bias and undercoverage. E) a multistage sample of varying cholesterol levels.

8 20. You are testing a new medication for relief of depression. You are going to give the new medication to subjects suffering from depression and see if their symptoms have lessened after a month. You have eight subjects available. Half of the subjects are to be given the new medication and the other half a placebo. The names of the eight subjects are given below. 1. Brian 5. Henry 2. Chris 6. Lauren 3. Dillon 7. Patrick 4. Fay 8. Tom Using the list of random digits starting at the beginning of this list and using single-digit labels, you assign the first four subjects selected to receive the new medication, while the remainder receive the placebo. The subjects assigned to the placebo are A) Chris, Dillon, Fay, and Lauren. B) Brian, Chris, Henry, and Tom. C) Brian, Chris, Dillon, and Fay. D) Henry, Lauren, Patrick, and Tom. E) Brian, Henry, Patrick, and Tom. Use the following to answer questions 21 and 22: A study of human development showed two types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching the different kinds of movies. One kind of movie was shown at 8 a.m. (right after the children had breakfast) and another at 11 a.m. (right before the children had lunch). It was found that during the movie shown at 11 a.m., more crackers were eaten than during the movie shown at 8 a.m.. The investigators concluded that the different types of movies had an effect on appetite.

9 21. The results cannot be trusted because A) the movies should not have been shown to younger children. B) children are usually too sleepy early in the morning to watch movies. C) the investigators should have used several bowls, with crackers randomly placed in each. D) the investigators were biased. They knew beforehand what they hoped the study would show. E) the time the movie was shown is a confounding variable. 22. The explanatory variable in this experiment is A) the number of crackers eaten. D) the different kinds of movies. B) the bowls. E) the time the movie was shown. C) the children in the study. Use the following to answer questions 23 and 24: A group of college students believes that herbal tea has remarkable restorative powers. To test their theory they make weekly visits to a local nursing home, visiting with residents, talking with them, and serving them herbal tea. After several months, many of the residents are more cheerful and healthy. 23. The response variable in this experiment is A) the herbal tea. B) the emotional state of the residents. C) the visits of the college students. D) the residents of the nursing home. E) the fact that this is a local nursing home. 24. The confounding variable in this experiment is A) the herbal tea. B) the emotional state of the residents. C) the visits of the college students. D) the time of day the tea was consumed. E) the fact that this is a local nursing home. 25. Two variables in a study are said to be confounded if A) one cannot separate their effects on a response variable. B) they are highly correlated. C) one does not explain the other. D) one of them is from a biased source. E) they do not have a normal distribution.

10 26. For one kindergarten class in her district, a researcher determines which children already can read simple words and which children cannot upon entering kindergarten. The children are followed until third grade, at which point they are tested to determine the grade level at which they are reading. Those children who were reading simple words on entering kindergarten are found to be reading at a higher level than those who could not read simple words on entering kindergarten. The researcher A) needs to check the reading level of the children's parents. B) needs to retest in sixth grade or no conclusions can be reached. C) needs to have taken a random sample of kindergarten students instead of one class to conclude a cause-and-effect relationship. D) can conclude that children should be taught to read in preschool, as there are clear benefits to reading early. E) cannot conclude that being able to read before entering kindergarten is beneficial, as there may be confounding variables in this study. 27. A basketball player makes 2/3 of his free throws. To simulate a single free throw, which of the following assignments of digits to making a free throw are appropriate? A) 2 and 3 correspond to making a free throw while all the other numbers correspond to missing a free throw. B) 01, 02, 03, 04, 05, 06 correspond to making the free throw and 07, 08, 09, and 10 correspond to missing the free throw. C) 0 and 1 correspond to making the free throw and 2 corresponds to missing the free throw. D) 1 and 2 correspond to making the free throw and 3 corresponds to missing the free throw. E) Both C) and D) are correct. 28. To simulate a basketball player who makes 60% of his free throws, we use the digits 1, 2, 3, 4, 5, and 6 to correspond to making the free throw while 7, 8, 9, and 0 correspond to missing the free throw. Assume successive shots are independent and we obtain the following sequence of 10 random digits: Using these digits, the relative frequency of making a free throw is A) 7/10 B) 1/10 C) 4/5 D) 3/5 E) 1/2 29. To simulate a single roll of a die, we can use the correspondence 1, 2, 3, 4, 5, and 6 in the table of random numbers. For two consecutive rolls, we can use the correspondence A) 1, 2, 3, 4, 5, 6, 7,, 35, 36 for 36 possible outcomes. B) 11, 22, 33, 44, 55, 66. C) 11, 12, 13, 14, 15, 16, 21,... 26,..., 61, 62, for 36 possible outcomes. D) None of the above are correct. E) A, B, and C are all correct.

11 Use the following to answer the remaining questions: To simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we win $2, if it takes us two tosses we win $1, and if we get two tails in a row we win nothing. Use the following sequence of random digits: The estimated probability of winning $2 in this game is A) 0 B) 1/3 C) 1/4 D) 7/11 E) 7/ The estimated probability of winning nothing is A) 2/11 B) 2/15 C) 6/15 D) 7/11 E) The estimated (expected) number of tosses in a single trial of the game is A) 0 B) 1 C) 15/7 D) 15/9 E) 15/ A sociologist wants to study the attitudes of American male college students toward marriage and husband and wife relations. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. All 25 complete and return the questionnaire. The sample in this situation is A) all men taking a comparable sociology class. B) all male students in the class planning on marriage. C) all the men in the Sociology 101 class. D) all married men in the Sociology 101 class. E) the 25 men who received and returned the questionnaire. 34. To simulate a basketball player who makes 50% of his free throws, we use the digits 1, 2, 3, 4, and 5 correspond to making the free throw while 6, 7, 8, 9, and 0 correspond to missing the free throw. Assume successive shots are independent and we obtain the following sequence of 10 random digits: Using these digits, the relative frequency of missing a free throw is A) 1/10 B) 1/9 C) 1/5 D) 2/5 E) 3/5 35. To simulate a basketball player who makes 90% of his free throws, we say the digits 1 through 9 correspond to making the free throw while 0 corresponds to missing the free throw. Assume successive shots are independent and we obtain the following sequence of 10 random digits: Using these digits, the relative frequency of missing a free throw is A) 1/10 B) 1/9 C) 1/6 D) 1/2 E) 0

12 Ch. 5 (Part I) Review Answers 1. C 2. E 3. A 4. D 5. E 6. E 7. B 8. B 9. A 10. E 11. A 12. B 13. D 14. A 15. A 16. E 17. E 18. B 19. D 20. A 21. E 22. D 23. B 24. C 25. A 26. E 27. E 28. A 29. C 30. D 31. A 32. E 33. E 34. D 35. E