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Chapter 11: Problem 15

Mistaken poll A local TV station conducted a "PulsePoll" about the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the late-night news. Based on the phone calls, the station predicted that Amabo would win the election with \(52 \%\) of the vote. They were wrong: Amabo lost, getting only \(46 \%\) of the vote. Do you think the station's faulty prediction is more likely to be a result of bias or sampling error? Explain.

Short Answer

Expert verified
The faulty prediction is more likely due to bias in the poll method.

Step by step solution

01

Understanding Bias and Sampling Error

Bias occurs when there is a systematic error that favors a particular outcome due to flawed data collection. Sampling error is the random variability between the sample and the actual population outcome. This can happen purely by chance when a sample is not perfectly representative of the overall population.
02

Analyzing the Poll Method

The poll was conducted by inviting TV viewers to call in their votes. This method is likely to produce a non-representative sample because it only includes viewers who were watching the evening news and were motivated to call. This is a classic example of selection bias.
03

Evaluation of Poll Results and Actual Results

The poll predicted Amabo would win with 52% but he received only 46%. The 6% difference between the poll prediction and actual results is significant. With a representative sample, a difference this large typically suggests systematic issues, not random chance.
04

Conclusion: Bias vs. Sampling Error

Considering the method used to collect poll responses (voluntary phone-in from TV viewers), there is a higher likelihood that the prediction error was due to bias rather than just sampling error. This is because voluntary polls often suffer from self-selection bias, where the participants are not representative of the general voter population.

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Key Concepts

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

Sampling Error
Sampling error is a common issue in polling and occurs when there is a discrepancy between the sample results and the true characteristics of the population. This error arises due to the random nature of selecting a sample rather than surveying the whole population. To visualize this, imagine you have a big jar full of marbles. If you randomly pick a handful without looking, the colors you pick might not perfectly represent the color proportions of the entire jar.
  • **Nature of Sampling Error**: It is unpredictable and random, meaning that by pure chance, some samples will differ from the actual population values.
  • **Size of Error**: The size of the sampling error generally decreases with larger sample sizes, as more data points provide a better representation of the population.
Thus, even with the best intentions, every sample carries a risk of sampling error unless the entire population is surveyed.
Selection Bias
Selection bias happens when the sample in a poll is not truly representative of the larger population. This leads to skewed or unbalanced results. In the given exercise, the poll was based on viewers who chose to call in, thereby introducing selection bias. Imagine conducting a survey in a dessert shop to determine the popularity of desserts among the general population. The results might suggest dessert is universally loved, but this is due to the biased sample selection 鈥� only dessert lovers are likely to be there!
  • **Voluntary Response Bias**: This is a specific type of selection bias found in polls where participants volunteer themselves. Typically, these individuals might have strong opinions, differing from the general populace.
  • **Examples**: If a political poll only questions people at a rally for a candidate, it won't reflect the wider population's views.
To avoid this, pollsters need to ensure the sample selection is random and inclusive.
Polling Methods
Polling methods refer to the various techniques used to gather data from people, and each method has its strengths and weaknesses. The method chosen can significantly affect the accuracy and reliability of the results. In the mentioned exercise, the method used was a phone-in poll, where viewers were invited to call a number and cast their vote. Though convenient, this method is often not the best for obtaining representative results.
  • **Types of Polling Methods**:
    • **Phone-in Polls**: Easy but usually biased as they exclude those not watching TV.
    • **Face-to-Face Interviews**: Time-consuming but can provide in-depth data.
    • **Online Surveys**: Cost-effective but may also exclude certain demographics.
  • **Method Suitability**: Choosing the right method depends on the population being studied, the resources available, and the required accuracy.
Understanding different polling methods helps in choosing the best one for specific research to ensure reliable results.
Non-representative Sample
A non-representative sample is one that does not accurately reflect the larger group from which it is drawn. This often leads to incorrect conclusions because the sample fails to capture the diversity or characteristics of the overall population. In the television poll, the respondents were likely not representative of all voters, as the sample came solely from TV viewers who were available and willing to call in.
  • **Consequences of Non-representative Samples**: They skew results and lead to incorrect predictions, just like predicting an election winner incorrectly.
  • **Causes**: Causes include incorrect sampling methods, insufficient sample size, or exclusion of significant demographic groups.
To ensure samples are representative, it's essential to use random sampling techniques and strive to include various population segments. This minimizes bias and sampling errors, providing more reliable and valid poll results.

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Most popular questions from this chapter

\- Banning ephedra An online poll at a website asked: A nationwide ban of the diet supplement ephedra went into effect recently. The herbal stimulant has been linked to 155 deaths and many more heart attacks and strokes. Ephedra manufacturer NVE Pharmaceuticals, claiming that the FDA lacked proof that ephedra is dangerous if used as directed, was denied a temporary restraining order on the ban yesterday by a federal judge. Do you think that ephedra should continue to be banned nationwide? \(65 \%\) of 17,303 respondents said "yes." Comment on each of the following statements about this poll: a) With a sample size that large, we can be pretty certain we know the true proportion of Americans who think ephedra should be banned. b) The wording of the question is clearly very biased. c) The sampling frame is all Internet users. d) Results of this voluntary response survey can't be reliably generalized to any population of interest.

Roadblock State police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. It would be too inconvenicnt and costly to check every vehicle that passes through a checkpoint, so they decide to stop about \(1 / 20\) of the vehicles. a) Why would a simple random sample be unreasonable for this situation. b) Identify two possible sampling schemes that could be used. Explain how randomization would be used in each.

. Quality control Sammy's Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, weighs the contents, and tastes the product. Help Sammy select the sample jars. Today's cases are coded 07N61 through 07N80. a) Carefully explain your sampling strategy. b) Show how to use random numbers to pick 3 jars. c) Did you get a simple random sample of the jars? Explain.

Toxic waste The Environmental Protection Agency took a map of a region near a former industrial waste dump and placed a grid of 552 squares on it. They randomly selected any 16 of those squares from which to collect soil samples and checked each for evidence of toxic chemicals. a) What type of sampling did they use? b) Is there any sort of bias associated with this sampling procedure? c) One researcher suggests that plots closer to the old dump site could contain more contaminants than those farther away. How could the sampling procedure be improved to take this into account

Texas A \& M Administrators at Texas A\&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A\&M student body has about 46,000 members. a) What problems do you see with asking the following question of students? "Are you the first member of your family to seck higher education?" b) For each scenario, identify the kind of sample used by the university administrators: i. Select several dormitories at random and contact everyone living in the selected dorms. ii. Using a computer-based list of registered students, contact 200 freshmen, 200 sophomores, 200 juniors, and 200 seniors selected at random from each class. iii. Using a computer-based alphabetical list of registered students, select one of the first 25 on the list by random and then contact the student whose name is 50 names later, and then every 50 names beyond that. c) A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because everyone had an equal opportunity to sit in any seat and because she randomized the choice of rows. What do you think? Be specific. d) For each of these proposed survey designs, identify the problem and the effect it would have on the estimate of the percentage of students who are the first in their family to go to college. i. Publish an advertisement inviting students to visit a website and answer questions. ii. Set up a table in the student union and ask students to stop and answer a survey. e) The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of current A\&M students who are the first in their families to attend college. Explain to the president the difference between the proportion of respondents who are first attenders and the proportion of the entire student body that are first attenders. Use appropriate statistics terminology.
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