中文
Problem 15
一家民意调查公司有兴趣对美国注册选民进行代表性抽样调查。该公司将抽样工作自动化，在美国境内随机拨打电话号码。每次
- 如果无人接听或电话答录机接通，则自动拨打另一个号码。
- 如果有人接听，调查人员会核实此人是否年满 18 岁。
- 如果该人未满 18 周岁，则不记录任何回复，并拨打另一个号码。
- 如果该人至少年满 18 岁，则对其进行调查。
有些人聲稱所使用的程序不允許把結果擴展到所有登記選民。
以下哪項不是對所使用程序的合理關注？
(A) 有 18 歲以下子女的登記選民在樣本中可能代表不足。
(B) 未登記電話號碼的登記選民可能在樣本中代表不足。
(C) 擁有一個以上電話號碼的登記選民可能在樣本中所佔比例過高。
(D) 居住在由一名以上選民組成的家庭中的登記選民可能代表性不足。
(E) 未登记投票的人可能会使抽样结果出现偏差。
Solution
公司使用一个程序，即随机拨打美国的电话号码。如果有未成年人接听电话，民意调查人员就会结束通话并继续前进。如果是成年人（18 岁或以上）接听，则对该成年人进行调查。问题为哪种潜在的担忧***不合法。
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**(A) 有 18 岁以下子女的登记选民可能代表不足。
- 由于未成年人接听电话会导致民意调查人员立即结束通话（永远不会再次拨打同一号码），因此有儿童接听电话的家庭有可能被排除在外。这是一个**合理的担忧。
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**(B) 未登记电话号码的登记选民可能代表性不足。
- 该公司使用的是随机电话号码生成，而不是 “列名 ”号码簿。未登记号码只是未在通讯录中公布的电话号码；但是，随机数字拨号可以以相同的概率拨到任何有效电话号码（已登记或未登记）。因此，如果程序真的是随机生成电话号码，那么没有特别的理由非列表号码的代表性不足。**这是 “不合法 ”问题的可能选择。
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**(C)拥有一个以上电话号码的登记选民可能比例过高。
- 如果一个人有多条线路（如家庭线路、工作线路、多部手机），他们就有更多机会被呼叫。因此，他们可能会代表性过高。这是一个合理的**问题。
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**(D)居住在有多于一名选民的家庭中的登记选民可能代表性不足。
- 如果一个家庭中有多个登记选民共用一个电话号码，那么只有最先接听电话并符合年龄要求的选民才能接受调查。该住户中的其他选民不会在这次通话中接受调查。这可能导致多选民家庭的代表性不足。这是合理的担忧。
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**(E)未登记投票的人可能会使抽样结果产生偏差。
- 民调机构只核实年龄（≥18 岁），而不核实登记状况。因此，未登记选民也可能接受调查，从而可能使结果出现偏差。这是合理的担忧。
因此，不合法的担忧（实际上不应该影响随机数字拨号下的抽样）是： > (B)
(B) 未登記電話號碼的登記選民可能在樣本中代表不足。
如果電話是打給隨機產生的號碼，他們的代表性不會有系統地偏低（因為未登記電話號碼仍然是有效的電話號碼，並會包括在隨機抽樣過程中）。
答案：(B)
因为随机拨号会拨打所有有效号码，所以 “非公开列表号码（unlisted telephone numbers）会被低估 ”这一点并不成立。
English
Problem 15
A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Each time a
• If there is no response or if an answering machine is reached, another number is automatically called.
• If a person answers, a survey worker verifies that the person is at least 18 years of age.
• If the person is not at least 18 years of age, no response is recorded, and another number is called.
• If the person is at least 18 years of age, that person is surveyed.
Some people claim the procedure being used does not permit the results to be extended to all registered voters.
Which of the following is NOT a legitimate concern about the procedure being used?
(A) Registered voters with children under the age of 18 years may be underrepresented in the sample.
(B) Registered voters with unlisted telephone numbers may be underrepresented in the sample.
(C) Registered voters who have more than one telephone number may be overrepresented in the sample.
(D) Registered voters who live in households consisting of more than one voter may be underrepresented.
(E) People who are not registered to vote may bias the sample results.
Analysis
The firm is using a procedure in which random phone numbers in the U.S. are called. If a minor answers, the pollster ends the call and moves on. If an adult (18 or older) answers, that adult is surveyed. We want to see which potential concern is NOT legitimate.
Let’s check each choice:
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(A) Registered voters with children under the age of 18 may be underrepresented.
- Since a minor answering the phone causes the pollster to immediately end the call (and never reattempt the same number), it’s possible that households with children answering could be dropped. This is a legitimate concern.
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(B) Registered voters with unlisted telephone numbers may be underrepresented.
- The firm is using random phone number generation, not a directory of “listed” numbers. Unlisted numbers are simply phone numbers not published in directories; however, random-digit dialing can reach any valid phone number (listed or unlisted) with equal probability. Thus, there is no particular reason for unlisted numbers to be underrepresented if the procedure truly generates phone numbers randomly. This is the likely choice for the “NOT legitimate” concern.
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(C) Registered voters who have more than one telephone number may be overrepresented.
- If an individual has multiple lines (e.g., home line, work line, multiple cell phones), they have more chances to be called. Hence they can be overrepresented. This is a legitimate concern.
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(D) Registered voters who live in households with more than one voter may be underrepresented.
- If there are multiple registered voters in one household sharing a single phone number, only whoever first picks up and meets the age requirement gets surveyed. The other voters in that household do not get surveyed on that call. This could underrepresent multi-voter households. Legitimate concern.
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(E) People who are not registered to vote may bias the sample results.
- The pollster verifies only age (≥18), not registration status. Thus, non-registered voters might also be surveyed, potentially biasing the results. Legitimate concern.
Hence, the NOT legitimate concern (the one that should not actually affect the sampling under random-digit dialing) is:
(B) Registered voters with unlisted telephone numbers may be underrepresented in the sample.
They would not be systematically underrepresented if calls are placed to randomly generated numbers (since unlisted numbers are still valid phone numbers and are included in the random selection process).
Answer: (B)
因为随机拨号会拨打所有有效号码，所以“非公开列表号码（unlisted telephone numbers）会被低估”这一点并不成立。