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Chapter 14: Problem 70

An article in the Providence Journal about automobile accident fatalities includes the following observation: "Fortytwo percent of all fatalities occurred on Friday, Saturday, and Sunday, apparently because of increased drinking on the weekends." (a) Give a possible argument as to why the conclusion drawn may not be justified by the data. (b) Give a different possible argument as to why the conclusion drawn may be justified by the data after all.

Short Answer

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(a) The conclusion is unjustified because it only considers one possible cause for the increased fatalities on weekends, without considering other factors like increased travel. (b) The conclusion could be justified if correlated with the known fact that alcohol consumption increases on the weekends and that alcohol impairs driving ability, making accidents more likely.

Step by step solution

01

Analysis of the presented statistic

Interpret the given statistic - 42% of all fatalities occurred on Friday, Saturday, and Sunday. This statistic only reflects the frequency of the accidents during these days. It does not provide any direct information about the cause, like 'increased drinking on the weekends'.
02

Provide a Possible Contradictory Argument (Part a)

Provide a different reason which contradicts the original conclusion. For example, one argument could be: the data does not specify the time of the accidents. The high rate of accidents could also be due to increased travel on weekends, not necessarily 'increased drinking.' Without more specific data, attributing the high rate of fatalities strictly to increased drinking is unfounded.
03

Formulate a Justifying Argument (Part b)

Even though the link between increased drinking and accident rate is not directly supported by the data, it can still be speculated based on background knowledge. Other studies have shown that alcohol consumption increases on weekends, and it's also well-documented that alcohol impairs driving ability. Therefore, it's reasonable to guess that the high rate of accidents on these days might be partly due to increased drinking.

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Key Concepts

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

Causal Inference
Understanding causal inference is crucial when analyzing statistical data. It involves deducing a cause-and-effect relationship from a dataset. The key challenge with causal inference is determining whether one event (such as increased drinking) directly causes another event (like increased automobile fatalities). In the exercise, a causal inference was drawn that weekend fatalities are high due to increased drinking. However, such conclusions can't be easily established from frequency data alone.

To make a valid causal inference:
  • We need evidence of a direct link between the purported cause and effect.
  • Controlled experimental data or more detailed observational data is often necessary.
  • Consider alternative explanations and variables that might affect the outcome to avoid biased conclusions.
Without concrete evidence showing a direct cause, in this case, the given conclusion might be speculative rather than inferentially sound.
Data Interpretation
Data interpretation is about extracting meaning and insights from collected data. It's an essential skill to understand what the numbers truly represent. In the original exercise, the statistic revealed that 42% of fatalities happen during weekends. However, interpreting this to mean that drinking is the cause requires careful consideration.

There are various factors to consider in proper data interpretation:
  • Look beyond surface-level numbers and explore deeper layers of information.
  • Consider context, such as the demographic or timing of data collection, which can influence outcomes.
  • Bridge the gap between raw numbers and theoretical assumptions cautiously, ensuring assumptions have supporting data.
In this scenario, other factors like increased weekend traffic might equally contribute to the observed pattern, highlighting the need for careful interpretation.
Statistical Reasoning
Statistical reasoning involves making sense of data through a logical and systematic approach, considering both evidence and uncertainty. This reasoning allows us to make informed judgments. The given situation involved reasoning about whether increased weekend fatalities are indeed linked to drinking.

Effective statistical reasoning requires:
  • Identifying patterns and trends and understanding their implications.
  • Using sound logical steps and understanding uncertainty and probability.
  • Being aware of potential biases and errors in data collection and interpretation.
In the exercise, one must determine the reasonableness of attributing accident spikes to drinking without direct causal evidence. Statistical reasoning can help consider these aspects and arrive at a well-rounded judgment.

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Most popular questions from this chapter

Refer to the following story (see also Exercise 32): The Dean of Students at Tasmania State University wants to determine how many undergraduates at TSU are familiar with a new financial aid program offered by the university. There are 15,000 undergraduates at \(T S U,\) so it is too expensive to conduct a census. The following sampling method, known as systematic sampling, is used to choose a representative sample of undergraduates to poll. Start with the registrar's alphabetical listing containing the names of all undergraduates. Randomly pick a number between 1 and \(100,\) and count that far down the list. Take that name and every 100 th name after it. For example, if the random number chosen is \(73,\) then pick the \(73 \mathrm{rd}, 173 \mathrm{rd}, 273 \mathrm{rd},\) and so forth, names on the list. (a) Suppose that the survey had a response rate of \(90 \%\) and that 108 students responded that they were not familiar with the new financial aid program. Give a statistic for the total number of students at the university who were not familiar with the new financial aid program. (b) Do you think the results of this survey will be reliable? Explain.

Question order bias. In July \(1999,\) a Gallup poll of 1061 people asked the following two questions: As you may know, former Major League Baseball player Pete Rose is ineligible for baseball's Hall of Fame because of charges that he gambled on baseball games. Do you think he should or should not be eligible for admission to the Hall of Fame? As you may know, former Major League Baseball player Shoeless Joe Jackson is ineligible for baseball's Hall of Fame because of charges that he took money from gamblers in exchange for fixing the 1919 World Series. Do you think he should or should not be eligible for admission to the Hall of Fame? The order in which the questions were asked was random: Approximately half of the people polled were asked about Rose first and Jackson second; the other half were asked about Jackson first and Rose second. When the order of the questions was Rose first and Jackson second, \(64 \%\) of the respondents said that Rose should be eligible for admission to the Hall of Fame and \(33 \%\) said that Jackson should be eligible for admission to the Hall of Fame. When the order of the questions was Jackson first and Rose second, \(52 \%\) said that Rose should be eligible for admission to the Hall of Fame and \(45 \%\) said that Jackson should be eligible for admission to the Hall of Fame. Explain why you think each player's support for eligibility was less (by \(12 \%\) in each case) when the player was second in the order of the questions.

Darroch's method. is a method for estimating the size of a population using multiple (more than two) captures. For example, suppose that there are four captures of sizes \(n_{1}, n_{2}, n_{3},\) and \(n_{4},\) respectively, and let \(M\) be the total number of distinct individuals caught in the four captures (i.e., an individual that is captured in more than one capture is counted only once). Darroch's method gives the estimate for \(N\) as the unique solution of the equation \(\left(1-\frac{M}{N}\right)=\left(1-\frac{n_{1}}{N}\right)\left(1-\frac{n_{2}}{N}\right)\left(1-\frac{n_{3}}{N}\right)\left(1-\frac{n_{4}}{N}\right)\). (a) Suppose that we are estimating the size of a population of fish in a pond using four separate captures. The sizes of the captures are \(n_{1}=30, n_{2}=15, n_{3}=22,\) and \(n_{4}=45 .\) The number of distinct fish caught is \(M=75 .\) Estimate the size of the population using Darroch's formula (b) Show that with just two captures Darroch's method gives the same answer as the capture-recapture method.

Refer to the following story: The 1250 students at Eureka High School are having an election for Homecoming King. The candidates are Tomlinson (captain of the football team), Garcia (class president), and Marsalis (member of the marching band). At the football game a week before the election, a pre- election poll was taken of students as they entered the stadium gates. Of the students who attended the game, 203 planned to vote for Tomlinson, 42 planned to vote for Garcia, and 105 planned to vote for Marsalis. Name the sampling method used for this survey.

A large jar contains an unknown number of red gumballs and 150 green gumballs. As part of a seventh-grade class project the teacher asks Carlos to estimate the total number of gumballs in the jar using a sample. Carlos draws a sample of 50 gumballs, of which 19 are red and 31 are green. Use Carlos' sample to estimate the number of gumballs in the jar.
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