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1 Chapter 2 Data Collection 2.1 Observation single data point. Variable characteristic about an individual. 2.2 Answers will vary. 2.3 a. categorical b. categorical c. discrete numerical d. continuous numerical e. discrete numerical f. continuous numerical (some may say discrete if referencing a food label.) g. continuous numerical 2.4 a. continuous numerical b. discrete numerical c. categorical d. continuous numerical e. categorical d. discrete numerical 2.5 Answers will vary. 2.6 Answers will vary. 2.7 a. ratio b. ordinal c. nominal d. interval e. ratio f. ordinal 2.8 a. ratio b. ratio c. interval d. nominal e. ordinal f. nominal 2.9 Answers will vary a. ordinal or interval b. ordinal c. nominal d. ratio 2.11 a. cross-sectional b. time series c. time series d. cross-sectional. 4
2 2.12 a. time series b. cross-sectional c. time series d. cross-sectional 2.13 a. time series b. cross-sectional. c. time series. d. cross-sectional Answers will vary a. Census. You can easily ask each of your friends this question. b. Census or Sample. If your class is large you might take a sample. c. Sample. The number of students at a university is too large to take a census. d. Census. You most likely have fewer than 7 classes so fewer than 7 professors a. Parameter. b. Parameter. c. Statistic. d. Statistic 2.17 a. Sample. Over the lifetime of your computer you will recharge your battery a very high number of times. A sample makes sense in this case. b. Census or sample. If your class is large you might take a sample. c. Sample. The number of students at a university is too large to take a census. d. Census. You can easily ask each of your friends this question Use the formula: N= 20*n a. N = 20*10 = 200 b. N = 20*50 = 1000 c. N = 20*100 = a. Convenience. b. Systematic. c. Judgment or biased a. In the rush to leave the theater, stop at the restroom, use their cell phone, etc. it would not be possible for everyone to have an equal chance to be included in the sample. But if we were to assign a random number to each seat and then design a random sample based on seat numbers, we could possibly obtain a simple random sample. Response rate might be low for the reasons already listed. b. Might only get those who didn t like the movie and couldn t wait to leave. There might not be a large enough crowd to get every 10 th person to be representative and leaving the theatre is not a linearly organized event. Might have underrepresented sample by only selecting those with earrings. c. Only those who liked the movie or really hated the movie might respond, a bias due to self-selection Answers will vary a b. Answers will vary. c. Due to random variation the sample may not be representative Answers will vary. 5
3 2.24 a. Response bias. The students might exaggerate the number of dates they ve had. b. Self-selection bias, coverage error. By only asking folks outside of a church you might get a number that is higher than the number from the general public. c. Coverage error, self-selection bias. Same reasons as in part b a. Telephone or web. A web-based survey might overestimate the number who prefer a web-based course. b. Direct observation of students on campus. c. Interview, web, or mail. Response rates would most likely differ with the three methods. Mail surveys tend to have lower response rates. d. Interview or web a. Mail or interview. A mail survey might have a lower response rate. b. Direct observation, through customer invoices/receipts. c. Mail. (See part a.) d. Interview Version 1: Most would say yes. Version 2: More varied responses Does not include all possible responses or allow for the responder to pick something other than those presented a. Continuous numerical. b. Categorical. c. Discrete numerical. d. Discrete numerical. e. Continuous numerical a. Ordinal (seeds represent a ranking of the players) b. Ratio c. Ratio d. Ratio e. Ratio, zero is meaningful Answers will vary Answers will vary Q1 Categorical, nominal. Q2 Continuous, ratio. Q3 Continuous, ratio. Q4 Discrete, ratio. Q5 Categorical, ordinal or interval. Q6 Categorical, ordinal or interval. Q7 Discrete, ratio. Q8 Continuous, ratio. Q9 Discrete, ratio. 6
4 Q10 Categorical, ordinal. Q11 Continuous, ratio. Q12 Discrete, ratio. Q13 Categorical, ordinal or interval. Q14 Categorical, nominal. Q15 Categorical, ordinal or interval a. Census. b. Sample. It would be too costly to track each can. c. Census. You can count them all quickly and cheaply. d. Census. This is assuming the company can easily generate the value from its human resource center a. Statistic. b. Parameter. c. Statistic. d. Parameter Answers will vary a. Number of employees or industry. b. There may be differences in profitability based on number of employees or industry type therefore we should be sure to take a sample that includes both types of industries. c. Under representation of chemical companies a. Cluster sampling. Easier to define geographic areas within a state where gasoline is sold. Gasoline stations are not everywhere, thus simple random sample or stratified sampling doesn t make sense. b. Population is finite Use mail or telephone. Census not possible a. Could use cluster sampling as grocery stores are in well defined locations. Identify clusters within each state. b. The sample frame is all stores in the US selling peanut butter. This population is very large, approaching infinity. c. A census is not possible given the size and scope of the investigation a. Cluster sampling b. Finite c. Yes a. No. It would have been too costly and taken too much time to observe everyone who used the restroom. b. The population is finite. c. Judgment or convenience d. Direct observation e. Interviewer bias a. Cluster Sampling b. It doesn t change the results but you cannot use the results to make conclusions about all salmon advertised as wild a. Answers will vary. b. Convenience. c. No. The population is too large. 7
5 d. Population can be treated as infinite a. Census this information is collected for all restaurants. b. Sample this cannot be tracked for all customers, must be taken from a sample. c. Sample this cannot be tracked for all customers, must be taken from a sample. d. Census this can be tracked on the point-of-sale system and will be population data Simple random sample or systematic sampling a. Judgment or convenience sample most likely although a SRS could have been conducted if the researcher had chosen a cluster to sample from. If a convenience sample then the statistic is not very accurate. b. Convenience, as accurate as the first statistic. c. SRS, fairly accurate. d. The statistic is most likely based on sales data reported by cigarette companies. While the data does not come from a random sample, this information is available for almost all companies and therefore fairly accurate. e. Based on US Census data, fairly accurate a. All 3 possible. Non-response bias is always present in surveys. Coverage error may occur since we don t know who has radar detectors and who doesn t before hand so may over represent one group. b. No causation shown so conclusions are not trustworthy a. Cluster sampling, neighborhoods are natural clusters. c. Picking a day near a holiday with heavy trash a. Convenience sampling. b. Based on such a small sample, that may not be representative of the entire population, it would be incorrect to make such a statement. c.perhaps, if the block is representative of the city, or area with in the city, or even in his local neighborhood, then such an inference might be valid, but confined to a specific geographic area. d. Coverage 2.51 a. Systematic b. Simple random sample c. Simple random sample or systematic d. Simple random sample or systematic e. Stratified 2.52 a. Systematic: every 5 th person who emerges from the office; or obtain data on n randomly selected patients and visits and analyze. b. Direct observation for a specific time period, such as all day Wednesday. c. n convenient places d. Last n flights e. Direct observation of gasoline prices at selected stations over a two week period a. Sales, store type b. Simple random sample 2.54 a. No, one has to sample because the population is infinite and unlistable. A census is not possible. b. One could stratify by state or county because geographic regions may differ a. No, the population is too large therefore sampling is required. b. Systematic Random sampling. A census is not possible because the population is too large. 8
6 2.57 Convenience sample because any other method would have been more expensive and time consuming a. Judgment or convenience sampling. b. Simple random sample would be impossible because it would be impossible to identify the individuals in the population Education and income could affect who uses the no-call list. a. They won t reach those who purchase such services. Same response for b and c Selection (only those who survived would be in the sample); coverage: may include those who were least exposed to such hazards a. Ordinal b. That the intervals are equal For each question, the difficulty is deciding what the possible responses should be and giving a realistic range of responses a. Rate the effectiveness of this professor. 1 Excellent to 5 Poor. b. Rate your satisfaction with the President s economic policy. 1 Very Satisfied to 5 Very dissatisfied. c. How long did you wait to see your doctor? Less than 15 minutes, between 15 and 30 minutes, between 30 minutes and 1 hour, more than 1 hour a. It depends on the questions asked. It is possible that more could agree the law should be upheld, even though on moral grounds they oppose it. b. Setting aside your moral and personal beliefs, given that abortion is legal, should the laws be upheld? Setting aside the fact that abortion is legal, do you believe that killing an unborn child is moral? c. Do you believe abortion should stay legal? 2.65 Answers will vary, one consideration would be to ask the questions as a yes or no and then provide a list of whys or ask the respondent to list reasons for yes or no answer Ordinal measure. There is no numerical scale and the intervals are not considered equal a. Likert scale. b. Should add a middle category that states Neither Agree Nor Disagree and remove Undecided category a. A constrained response scale. b. A Likert scale would be better. c. Self-selection bias. People with very bad experiences might respond more often than people with acceptable experiences. 9
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