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Solutions to End-of-Section and Chapter Review Problems 1 CHAPTER 1 1.1 (a) The types of beverages sold yield categorical or ―qualitative‖ responses. (b) The types of beverages sold yield distinct categories in which no ordering is implied. 1.2 Three sizes of soft drink are classified into distinct categories—small, medium, and large— in which order is implied. 1.3 (a) The time it takes to download an MP3 file from the internet yields numerical or ―quantitative‖ responses. (b) The download time is a ratio scaled variable because the true zero point in the measurement is zero unit of time. 1.4 (a) numerical, discrete, ratio scale (g) categorical, nominal scale (b) categorical, nominal scale (h) numerical, discrete, ratio scale (c) numerical, discrete, ratio scale (i) numerical, continuous, ratio scale (d) numerical, continuous, ratio scale (j) categorical, nominal scale (e) categorical, nominal scale (k) categorical, nominal scale (f) numerical, continuous, ratio scale 1.5 (a) numerical, continuous, ratio scale (f) categorical, nominal scale (b) numerical, discrete, ratio scale (g) categorical, nominal scale (c) numerical, continuous, ratio scale (h) numerical, discrete, ratio scale (d) categorical, nominal scale (i) categorical, nominal scale (e) categorical, nominal scale (j) categorical, nominal scale 1.6 (a) categorical, nominal scale (e) numerical, discrete, ratio scale (b) numerical, continuous, ratio scale (f) numerical, discrete, ratio scale (c) numerical, continuous, ratio scale (g) numerical, continuous, ratio scale (d) categorical, nominal scale (h) categorical, nominal scale 1.7 (a) numerical, continuous, ratio scale (e) categorical, nominal scale (b) numerical, discrete, ratio scale (f) numerical, discrete, ratio scale (c) categorical, nominal scale (g) categorical, nominal scale (d) numerical, continuous, ratio scale 1.8 (a) categorical, nominal scale (i) numerical, continuous, ratio scale * (b) categorical, nominal scale (j) numerical, continuous, ratio scale * (c) numerical, continuous, interval scale (k) categorical, nominal (d) numerical, continuous, ratio scale * (l) numerical, discrete, ratio scale (e) categorical, nominal scale (m) numerical, continuous, ratio scale * (f) categorical, nominal scale (n) numerical, continuous, ratio scale (g) numerical, discrete, ratio scale ** (o) categorical, nominal scale (h) numerical, discrete, ratio scale (p) numerical, continuous, ratio scale* *Some researchers consider money as a discrete numerical variable because it can be ―counted.‖ **Some researchers would ―measure" the time since starting the job and consider this a continuous numerical variable. 2 Chapter 1: Introduction and Data Collection 1.9 (a) In the first format, the measurement level is in ratio scale. In the second format, the measurement level is in ordinal scale. (b) Income may be considered discrete if we ―count‖ our money. It may be considered continuous if we ―measure‖ our money; we are only limited by the way a country's monetary system treats its currency. (c) The first format is preferred because the responses represent data measured on a higher scale. (d) The second format is less threatening to a respondent and likely leads to a greater response rate. 1.10 While it is theoretically true that ties cannot occur with continuous data, the grossness of the measuring instruments used often leads to the reporting of ties in practical applications. Hence two students may both score 90 on an exam—not because they possess identical ability but rather because the grossness of the scoring method used failed to detect a difference between them. 1.11 The director of market research would have access to the list of the department store's credit card customers. The females on the list would provide an immediate and convenient population frame. A questionnaire could be devised that is mailed with the monthly bill. The survey results could be validated through a comparison of responses to questionnaires distributed to a sample of non-credit card customers making clothing purchases. To expand the population frame beyond this by including all women residing in the metropolitan area would likely be unnecessarily costly and inefficient. 1.12 Operational definitions of fast service in a fast-food restaurant will differ. Fast service could be defined in terms of: a customer’s satisfaction level with service time, the number of minutes elapsed between entering the restaurant and receiving the completed order as measured by the customer, or the number of minutes elapsed between placing and filling the order as measured by the counter clerk. 1.13 (1) Place an X in the circle corresponding to your personal income last year. Under $20,000 $20,000 – $39,999 $40,000 or more (2) To the nearest thousand dollars, what was your household income last year? (3) What Adjusted Gross Income did you report on your federal income tax last year? Solutions to End-of-Section and Chapter Review Problems 3 1.14 (a) A teacher who has received an average score of above 4.5 on a 5-point scale evaluation scores given by the students at the end of a semester. (b) The sales generated by a worker that is above a certain threshold. (c) The level of satisfaction with a day that is above 4 on an ordinal scale of 1 through 5. (d) The number of minutes elapsed between entering the bank and receiving a service is less than a certain threshold. (e) Someone who has received at least 75% of the votes from co-workers to be a person who can effectively motivate, organize and maintain an amiable working atmosphere in a team environment. (f) The number of minutes elapsed between leaving the house and arriving at the office or school entrance. (g) A quarterback who has achieved a reception rate of more than 50%. 1.15 (a) A person who receives a score of 8 or above on a 10-point ordinal scaling. (b) A class that receives an average evaluation score of below 2.0 on a 5-point ordinal scaling. (c) A book that receives an average evaluation score of above 8 on a 10-point ordinal scaling. (d) A performance that has received a score of above 9 on a 10-point ordinal scaling. (e) A person who is responsible for the performance of a certain number of subordinates. (f) A plane that arrives within 2 minutes of the schedule arrival time. (g) The average amount of time measured to the closest minute spent on class related activities outside the lectures. 1.16 (a) (1) How many years of schooling have you completed? (2) What is the highest degree that you have earned? (3) Indicate the highest level of education attained: (a) Elementary School (b) Some High School (c) High School Diploma (d) Some College (e) Bachelor's Degree (f) Some Graduate School (g) Master's degree (h) Work on Doctorate (i) Doctoral Degree (j) Post-Doctoral Studies (b)-(c) Questions (1) or (2) could be asked in a personal or a telephone interview. Question (3) should not be considered for inclusion on a personal or telephone interview because it has too many options for respondents to remember precisely without having a printed list of options to scan as they respond. Question (1) has some amount of ambiguity in it. Ambiguities include that postsecondary work may be undertaken on a part-time basis, clouding the definition of what counts as years of schooling, and may include job-related training, clouding the definition of what constitutes schooling. Depending on the overall context, Question (2) could raise a respondent’s sensitivities. The potential for ambiguity and respondent sensitivity are reasons these questions should be posed interactively by a trained interviewer. (d) Although Question (3) may be the longest question of the three, it has the greatest clarity and thus may be the best question to pose on a mail survey. Clarity is particularly important to a mail survey because the survey respondent does not have the option of asking an interviewer for further clarification. 4 Chapter 1: Introduction and Data Collection 1.17 (a) 001 (b) 040 (c) 902 1.18 Sample without replacement: Read from left to right in 3-digit sequences and continue unfinished sequences from end of row to beginning of next row. Row 05: 338 505 855 551 438 855 077 186 579 488 767 833 170 Rows 05-06: 897 Row 06: 340 033 648 847 204 334 639 193 639 411 095 924 Rows 06-07: 707 Row 07: 054 329 776 100 871 007 255 980 646 886 823 920 461 Row 08: 893 829 380 900 796 959 453 410 181 277 660 908 887 Rows 08-09: 237 Row 09: 818 721 426 714 050 785 223 801 670 353 362 449 Rows 09-10: 406 Note: All sequences above 902 are discarded. 1.19 (a) Row 29: 12 47 83 76 22 99 65 93 10 65 83 61 36 98 89 58 86 92 71 Note: All sequences above 93 and all repeating sequences are discarded. (b) Row 29: 12 47 83 76 22 99 65 93 10 65 83 61 36 98 89 58 86 Note: All sequences above 93 are discarded. Elements 65 and 83 are repeated. 1.20 A simple random sample would be less practical for personal interviews because of travel costs (unless interviewees are paid to attend a central interviewing location). 1.21 This is a random sample because the selection is based on chance. It is not a simple random sample because A is more likely to be selected than B or C. 1.22 Here all members of the population are equally likely to be selected (unlike Problem 1.21) and the sample selection mechanism is based on chance. But selection of two elements is not independent; for example, if A is in the sample, we know that B is also, and that C and D are not. 1.23 (a) Since a complete roster of full-time students exists, a simple random sample of 200 students could be taken. If student satisfaction with the quality of campus life randomly fluctuates across the student body, a systematic 1-in-20 sample could also be taken from the population frame. If student satisfaction with the quality of life may differ by gender and by experience/class level, a stratified sample using eight strata, female freshmen through female seniors and male freshmen through male seniors, could be selected. If student satisfaction with the quality of life is thought to fluctuate as much within clusters as between them, a cluster sample could be taken. (b) A simple random sample is one of the simplest to select. The population frame is the registrar’s file of 4,000 student names. (c) A systematic sample is easier to select by hand from the registrar’s records than a simple random sample, since an initial person at random is selected and then every 20th person thereafter would be sampled. The systematic sample would have the additional benefit that the alphabetic distribution of sampled students’ names would be more comparable to the alphabetic distribution of student names in the campus population. Solutions to End-of-Section and Chapter Review Problems 5 1.23 (d) If rosters by gender and class designations are readily available, a stratified sample cont. should be taken. Since student satisfaction with the quality of life may indeed differ by gender and class level, the use of a stratified sampling design will not only ensure all strata are represented in the sample, it will generate a more representative sample and produce estimates of the population parameter that have greater precision. (e) If all 4,000 full-time students reside in one of 20 on-campus residence halls which fully integrate students by gender and by class, a cluster sample should be taken. A cluster could be defined as an entire residence hall, and the students of a single randomly selected residence hall could be sampled. Since the dormitories are fully integrated by floor, a cluster could alternatively be defined as one floor of one of the 20 dormitories. Four floors could be randomly sampled to produce the required 200 student sample. Selection of an entire dormitory may make distribution and collection of the survey easier to accomplish. In contrast, if there is some variable other than gender or class that differs across dormitories, sampling by floor may produce a more representative sample. 1.24 (a) Row 16: 2323 6737 5131 8888 1718 0654 6832 4647 6510 4877 Row 17: 4579 4269 2615 1308 2455 7830 5550 5852 5514 7182 Row 18: 0989 3205 0514 2256 8514 4642 7567 8896 2977 8822 Row 19: 5438 2745 9891 4991 4523 6847 9276 8646 1628 3554 Row 20: 9475 0899 2337 0892 0048 8033 6945 9826 9403 6858 Row 21: 7029 7341 3553 1403 3340 4205 0823 4144 1048 2949 Row 22: 8515 7479 5432 9792 6575 5760 0408 8112 2507 3742 Row 23: 1110 0023 4012 8607 4697 9664 4894 3928 7072 5815 Row 24: 3687 1507 7530 5925 7143 1738 1688 5625 8533 5041 Row 25: 2391 3483 5763 3081 6090 5169 0546 Note: All sequences above 5000 are discarded. There were no repeating sequences. N 5,000 (b) k 100 n 50 089 189 289 389 489 589 689 789 889 989 1089 1189 1289 1389 1489 1589 1689 1789 1889 1989 2089 2189 2289 2389 2489 2589 2689 2789 2889 2989 3089 3189 3289 3389 3489 3589 3689 3789 3889 3989 4089 4189 4289 4389 4489 4589 4689 4789 4889 4989 (c) With the single exception of invoice #0989, the invoices selected in the simple random sample are not the same as those selected in the systematic sample. It would be highly unlikely that a random process would select the same units as a systematic process. 1.25 (a) The proposed sample design is a nonprobability quota sample. Since the invoices are already separated into strata, a stratified sample should be used to reduce selection bias and improve generalizability of results. (b) Sampling 4% of the invoices in each of the four strata would produce a sample with the same number of units. (c) The proposed sample design is not a simple random sample because all invoices do not have an equal chance of being selected. 6 Chapter 1: Introduction and Data Collection 1.26 Before accepting the results of the survey on the effect of gender on online purchases, you might want to know, for example: Who funded the survey? Why was it conducted? What was the population from which the sample was selected? What sampling design was used? What mode of response was used: a personal interview, a telephone interview, or a mail survey? Were interviewers trained? Were survey questions field-tested? What type of online purchases were being considered? What questions were asked? Were they clear, accurate, unbiased, valid? What results indicate that males were more likely to make purchases online than females? What was the response rate? 1.27 Before accepting the results of a survey of college students, you might want to know, for example: Who funded the survey? Why was it conducted? What was the population from which the sample was selected? What sampling design was used? What mode of response was used: a personal interview, a telephone interview, or a mail survey? Were interviewers trained? Were survey questions field-tested? What questions were asked? Were they clear, accurate, unbiased, valid? What operational definition of ―vast majority‖ was used? What was the response rate? 1.28 (a) Possible coverage error: Only employees in a specific division of the company were sampled. (b) Possible nonresponse error: No attempt is made to contact nonrespondents to urge them to complete the evaluation of job satisfaction. (c) Possible sampling error: The simple random sample included a significantly higher proportion of female employees than the company list of full-time employees indicated. (d) Possible measurement error: The person collecting and analyzing the job satisfaction information has a major impact on the company’s merit pay decisions. 1.29 Before accepting the results of the poll conducted by Creative Group, you might want to know, for example: Who funded the study? Why was it conducted? What was the population from which the sample was selected? What was the sample size? What sampling design was used? What mode of response was used: a personal interview, a telephone interview, or a mail survey? Were interviewers trained? Were survey questions field-tested? What operational definition of "most creative in the morning" was used? What questions were asked? Were they clear, accurate, unbiased, valid? What was the response rate? Solutions to End-of-Section and Chapter Review Problems 7 1.30 Before accepting the results of the consumer expenditure survey, you might want to know, for example: Who funded the study? Why was it conducted? What was the population from which the sample was selected? What was the sample size? What sampling design was used? What mode of response was used: a personal interview, a telephone interview, or a mail survey? Were interviewers trained? Were survey questions field-tested? What operational definition of "spending on eating away from home" was used? What questions were asked? Were they clear, accurate, unbiased, valid? What was the response rate? 1.31 A population contains all the items whereas a sample contains only a portion of the items in the population. 1.32 Statistic is a summary measure computed from a sample whereas a parameter is a summary measure computed from an entire population. 1.33 Descriptive methods deal with the collection, presentation, summarization, and analysis of data whereas inferential methods deal with decisions arising from the projection of sample information to the characteristics of a population. 1.34 Statistics is useful because a manager needs to know how to properly present and describe information, how to draw conclusions about large populations based only on information obtained from samples, how to improve processes, and how to obtain reliable forecasts. 1.35 The development of computer technology has eliminated the computational barriers to using statistics, and makes these methods more accessible to more people. 1.36 The expanding needs of the census helped spark the development of tabulating machines at the beginning of the twentieth century. This achievement led to the development of large- scale mainframe computers and eventually to the personal computer. 1.37 Categorical random variables yield categorical responses, such as yes or no answers. Numerical random variables yield numerical responses such as your height in inches. 1.38 Discrete random variables produce numerical responses that arise from a counting process. Continuous random variables produce numerical responses that arise from a measuring process. 1.39 A nominal scale classifies data into various distinct categories in which no ordering is implied whereas an ordinal scale classifies data into distinct categories in which ordering is implied. 1.40 An interval scale is an ordered scale in which the difference between measurements is a meaningful quantity that does not involve a true zero point. A ratio scale is an ordered scale in which the difference between the measurements involve a true zero point. 8 Chapter 1: Introduction and Data Collection 1.41 An operational definition is a universally accepted definition that provides meaning to a concept or variable and can be communicated to other individuals. It is important because without it, the data collected can be flawed by ambiguities that arise from misinterpretation of the questions ask in a survey. 1.42 Data are needed to provide the input to a study or survey, to measure performance of a process, to evaluate conformance to standards, to assist in deciding among alternative courses of action, and to satisfy our curiosity. 1.43 A probability sample is one in which the individuals or items are selected based on known probabilities. A nonprobability sample is one in which the individuals or items are selected without regard to their probability of occurrence. 1.44 Fishbowl methods of sampling do not allow for a thorough mixing of items. 1.45 Sampling with replacement means that once a person or item is selected, it is returned to the frame where it has the same probability of being selected again. Sampling without replacement means that a person or item once selected is not returned to the frame and therefore cannot be selected again. 1.46 In a simple random sample, each individual item is selected randomly. In a systematic sample, the N individuals or items in the population frame are partitioned into k groups by dividing the size of the population frame N by the desired sample size n. The first individual or item to be selected is chosen at random from the k individuals or items in the first partitioned group in the population frame, and the rest of the sample is obtained by selecting every kth individual or item thereafter from the entire population frame listing. 1.47 In a stratified sample, the N individuals or items in the population are first subdivided into separate subpopulations, or strata, according to some common characteristic. In a systematic sample, the N individuals or items in the population frame are partitioned into k groups by dividing the size of the population frame N by the desired sample size n. The first individual or item to be selected is chosen at random from the k individuals or items in the first partitioned group in the population frame, and the rest of the sample is obtained by selecting every kth individual or item thereafter from the entire population frame listing. 1.48 In a stratified sample, the N individuals or items in the population are first subdivided into separate subpopulations, or strata, according to some common characteristic. In a cluster sample, the N individuals or items in the population are divided into several clusters so that each cluster is representative of the entire population. A random sampling of clusters is then taken and all individuals or items in each selected cluster are then studied. Solutions to End-of-Section and Chapter Review Problems 9 1.49 Coverage error occurs if we exclude certain groups of subjects from this population listing so that they have no chance of being selected in the sample. Coverage error results in a selection bias. If the listing is inadequate because certain groups of subjects in the population were not properly included, any random probability sample selected will provide an estimate of the characteristics of the target population, not the actual population. Nonresponse error arises from the failure to collect data on all subjects in the sample and results in a nonresponse bias. Sampling error reflects the heterogeneity, or ―chance differences,‖ from sample to sample based on the probability of particular individuals or items being selected in the particular samples. Measurement error refers to inaccuracies in the recorded responses. 1.55 Even though internet polling is less expensive, faster and offers higher response rates than telephone surveys, it is a self-selection response method. Because respondents who choose to participate in the survey do not usually represent the view of the public, the data collected is not appropriate for making inference about the general population. 1.56 (a) Source of the data: survey result (b) The answer to "Whether the CEO was required to give approval before starting the projects?" is a categorical random variable. (c) The average budget for these projects is a numerical random variable. (d) Sampling method: simple random sample. (e) The researchers are most likely to encounter sampling error and nonresponse bias. 1.57 (a) Population for the Goldman Sachs survey is all the U.S. households. (b) Population for Cyber Dialogue survey is all the people who have tried and quit online banking. (c) Cyber Dialogue could have constructed a frame for their survey from the combined list of customers, who tried online banking, of the banks that offered them. (d) They could have drawn a simple random sample or systematic sample from the frame if the characteristics of the customers were randomly distributed across the various banks that offered online banking. If customer characteristics were randomly distributed within and across banks, a cluster sample would be easier to collect. But if different bank attracted different types of customers, a stratified sample would be a better representation of the population. (e) The response will be categorical. (f) This is a statistic. 1.58 (a) Population: All online shoppers. (b) The researcher can conduct an online survey through the web sites of online shops. (c) To minimize non-response error in this type of survey, some form of incentives, e.g. offering a certain percentage of discount on a subsequent purchase, can be provided for completing the survey. (d) Sampling error can be reduced by increasing the response rate and, hence, the sample size of the survey. Any incentive that increases the response rate will reduce the sampling error. (e) Besides avoiding ambiguous wording and "leading questions", the survey can also request the respondent to provide email address in the survey so that random callbacks can be performed if needed to ascertain the reliability of the responses. 10 Chapter 1: Introduction and Data Collection 1.59 (a) The target population is all customers who, over the past 12 months, purchased a videocassette recorder manufactured by the consumer electronics company. (b) The sample frame is all customers who, over the past 12 months, returned a warranty card from the purchase of a videocassette recorder manufactured by the consumer electronics company. (c) Not all customers routinely return warranty cards. Nonrespondents introduce bias in the results of the survey. (d) (1) What is your gender? (2) Are you the head of the household? (3) How satisfied are you with the videocassette recorder? (e) (1) How many electronic products purchased from this company do you currently owned? (2) How many times have you brought your videocassette recorder in for some form of service since your purchased? (3) How many hours per week on the average do you use your videocassette recorder? (f) Each videocassette recorder warranty card can be assigned a number and a random sample can be drawn using the Table of Random Numbers. (g) The manager should use a stratified sample. The warranty cards should be divided into strata according to the different brands. The percentage of each brand in the frame should be recorded. A random sample of size corresponding to the percentage in the frame should then be selected from each of the strata. 1.60 (a) Population: Actual voters (b) Sample: "Exit" poll enables an estimate based on actual voters (c) This is superior to a prior telephone poll of registered voters because not all registered voters will actually vote. 1.61 (a) One more category to make them correspond to "very good", "good", "average", "poor", "very poor" will probably be more desirable. (b) Another "frown face" to balance the two "smile faces" will improve the questionnaire instrument because that will provide a middle point of reference. (c) Such self-selecting surveys are prone to coverage error because those customers who choose to respond are more likely to be the dissatisfied customers. There is less incentive for the satisfied customers to response to the survey because a satisfactory level of service is naturally expected when customers pay for the room. (d) The hotel has the complete list of guests from their registration. A random sample can be drawn from this frame. (e) A categorical question could be "Will you come back and visit us again?" (f) A numerical question could be "What is your household's annual income accurate to the nearest thousands of dollars?" 1.62 (a) Population: Cat owners (b) Sample frame: Households in the United States (d) (1) categorical (3) numerical (2) categorical (4) categorical TP1.1 (a) categorical (f) two continuous numerical measurements (b) categorical (g) categorical (c) categorical (h) categorical (d) continuous numerical (i) categorical (e) discrete numerical (j) continuous numerical

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