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Chapter 8: Problem 24

A sample of households in a community is selected at random from the telephone directory. In this community, \(4 \%\) of households have no telephone, \(10 \%\) have only cell phones, and another \(25 \%\) have unlisted telephone numbers. The sample will certainly suffer from (a) nonresponse. (b) undercoverage. (c) false responses.

Short Answer

Expert verified
Undercoverage (b) is the main issue.

Step by step solution

01

Understanding the Context

The problem gives us a scenario where a sample is selected from a telephone directory to study households. However, some households either don't have a phone, only have cell phones, or have unlisted numbers.
02

Identifying What a Telephone Directory Contains

A telephone directory typically contains listed landline numbers. It does not include households without phones, those only with cell phones, or those with unlisted numbers.
03

Defining Terms

Nonresponse refers to when a selected subject does not respond to the survey. Undercoverage occurs when some groups in the population are not represented. False responses occur when participants provide incorrect information.
04

Analyzing the Type of Bias

Given that the telephone directory is missing certain groups (households with no phones, only cell phones, or unlisted numbers), these groups are not adequately sampled. This means parts of the population are not fully covered by the survey.
05

Determining the Type of Survey Error

Since groups are missing from the sample due to the selection from a telephone directory, this leads to undercoverage, as not all segments of the population have a chance to be included.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Telephone Survey
A telephone survey is a method of collecting data by speaking directly with individuals over the phone. This type of survey used to be quite popular due to its convenience and cost-effectiveness. However, changes in technology and communication preferences have made it less effective in some cases.
  • Landline numbers are usually listed in telephone directories, making them easy targets for survey samples.
  • Many people now use cell phones exclusively, which are rarely listed in directories, leading to incomplete samples.
  • Unlisted numbers and households without phones also pose challenges for this method.
Moreover, telephone surveys can suffer from various biases such as selection bias, which can be critical when aiming to represent a whole population accurately. In modern contexts, combining telephone surveys with other methods, such as online or in-person surveys, might lead to more comprehensive results.
Undercoverage
Undercoverage occurs in survey sampling when some members of the population have little or no chance of being included in the sample. This typically arises from the method used to select participants. For example, using only a telephone directory to select households will likely lead to undercoverage.
  • The population segments without phones won't be included at all.
  • Households with only cell phones or unlisted numbers will also be excluded.
  • Undercoverage can result in unrepresentative samples that skew results and affect the survey's validity.
Addressing undercoverage is vital for ensuring that survey results are reliable and reflect the true characteristics of the entire population. Solutions can include diversifying data collection methods, such as using online surveys or face-to-face interviews, to reach underrepresented groups.
Population Representation
Population representation refers to the extent to which a sample used in a survey accurately reflects the larger population being studied. Achieving good representation is crucial for the validity of survey findings.
  • Sampling methods should ensure every subgroup within the population is adequately covered.
  • This means identifying the different segments and understanding their communication channels.
  • Effective representation leads to more reliable and generalizable data.
When selecting a sample, it's essential to consider potential biases and barriers to participation, such as undercoverage and nonresponse, which may distort the true representation. By understanding the population's makeup and employing diverse sampling techniques, better representation and more accurate survey results can be achieved.

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Most popular questions from this chapter

Your own bad questions. Write your own examples of bad sample survey questions. (a) Write a biased question designed to get one answer rather than another- (b) Write the "same question" in two different ways to get different responses. (c) Write a question to which many people may not give truthful answers.

The Pew Research Centers Report entitled "How Americans value public libraries in their communities, " released December 11, 2013, asked a random sample of 6224 Americans aged 16 and over, "Have you used a Public Library website in the last 12 months?" In the entire sample, \(30 \%\) said Yes. But only \(17 \%\) of those in the sample over 65 years of age said Yes. Which of these two sample percents will be more accurate as an estimate of the truth about the population? (a) The result for those over 65 is more accurate because it is easier to estimate a proportion for a small group of people. (b) The result for the entire sample is more accurate because it comes from a larger sample. (c) Both are equally accurate because both come from the same sample.

The National Health and Nutrition Examination Study (NHANES) had a random sample of 9317 participants recall their diet over the last 24 hours. The information in this sample was used in a recent study that found that, on average, \(57.9 \%\) of the calories eaten by participants were obtained from ultraprocessed foods, which include substances not used in culinary preparations such as flavors, colors, sweeteners, emulsifiers, and other additives. One of the limitations of the study reported by the authors was the dependence on the dietary recall of individuals. \({ }^{20}\) The authors were concerned with (a) response bias. (b) undercoverage. (c) overstratification.

Airport Shuttle. Blue Ribbon taxis offers shuttle service to the nearest airport. You look up the online reviews for Blue Ribbon taxis and find that there are 17 reviews, six of which report that the taxi never showed up. Is this a biased sampling method for obtaining customer opinion on the taxi service? If so, what is the likely direction of bias? Explain your reasoning carefully.

Student opinions. A university has 30,000 undergraduate and 10,000 graduate students. A survey of student opinion concerning health care benefits for domestic partners of students selects 300 of the 30,000 undergraduate students at random and then separately selects 100 of the 10,000 graduate students at random. The 400 students chosen make up the sample. (a) What is the probability that any of the 30,000 undergraduates is in your random sample of 300 undergraduates selected? What is the probability that any of the 10,000 graduate students is in your random sample of 100 graduate students selected? (b) If you have done the calculations correctly in part (a), the probability of any student at the university being selected is the same. Why is your sample of 400 students from the university not an SRS of students? Explain.
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