Scenario 21-1. In honor of Nidhi and her enduring respect for bridges, we have a series of questions featuring a bridge on today's test. Below is an xkcd comic by the inimitable Randall Munro. Although the characters are not clearly designated, suppose it is a conversation between a parent and a teenager. Read the comic and then use it to answer the following questions.

https://xkcd.com/1170/

Assume that the teenager and their mother are discussing a hypothesis test that reads as follows:

H0: It is safer to stay on the bridge than to jump off it and go splat.

HA: The bridge is on fire or otherwise dangerous; it is better to jump off it and hope for the best.

In this scenario, the actions of the teenager’s friends can be considered as evidence to be weighed in order to decide whether to reject the null hypothesis.

Refer to Scenario 21-1. Who is more afraid of a Type I error, the teenager or their mother?

Question

Scenario 21-1. In honor of Nidhi and her enduring respect for bridges, we have a series of questions featuring a bridge on today's test. Below is an xkcd comic by the inimitable Randall Munro. Although the characters are not clearly designated, suppose it is a conversation between a parent and a teenager. Read the comic and then use it to answer the following questions.

https://xkcd.com/1170/

Assume that the teenager and their mother are discussing a hypothesis test that reads as follows:

H0:  It is safer to stay on the bridge than to jump off it and go splat.

HA: The bridge is on fire or otherwise dangerous; it is better to jump off it and hope for the best.

In this scenario, the actions of the teenager’s friends can be considered as evidence to be weighed in order to decide whether to reject the null hypothesis.

Refer to Scenario 21-1. Who is more afraid of a Type I error, the teenager or their mother?

BlackTom AI · Accepted Answer

We begin by restating the core setup: Scenario 21-1 presents a hypothesis test about whether it is safer to stay on the bridge (H0) or to jump off (HA). The question asks who is more afraid of a Type I error, given that the teenager’s friends’ actions serve as evidence to weigh in on whether to reject H0.

First, recall what a Type I error means in this context: rejecting the null hypothesis H0 when it is actually true. In practical terms, that would mean deciding to jump off the bridge (rejecting H0) when, in fact, it would have been safer to stay on the bridge.

Option analysis (noting that the provided data lacks explicit multiple-choice options):
- Since there are no enumerated choices, we rely on the intended answer given: Mother. The reasoning follows that the mother, being more cautious and protective, would be more averse to a Type I error. She would fear wrongly concluding it is better to jump when staying on the bridge is actually safer. This corresponds to the risk of acting on a false belief about safety, potentially leading to a dangerous outcome.
- If we consider alternative reasoning, the teenager may be more willing to accept risk and more tolerant of Type I error, viewing a jump as a potential bold or necessary action. The teenager might downplay the harm from a false positive (believing jumping is justified even if not safer), thereby displaying less fear of making a Type I error.

Why the mother’s fear aligns with Type I error concerns: in statistical decision-making terms, the cost of a Type I error is high when the consequence is catastrophic or dangerous. Here, jumping off a bridge is physically hazardous; accusing the bridge as ‘unsafe to stay on’ (reject H0) when it is actually safe would lead to a severe real-world harm. The mother’s protective stance makes her more anxious about making a wrong call that could cause harm, i.e., about a Type I error.

Why the teenager might appear less concerned about Type I error: from a risk-tolerant perspective, the teenager could view jumping as a potential solution or an act of bravado, thereby assigning relatively lower cost to a false rejection of H0. This attitude reduces fear of Type I error relative to the mother.

In summary, the reasoning points to the mother as the one who would be more afraid of committing a Type I error, because the cost of incorrectly deciding to jump (when it would have been safer to stay) is high and aligns with a protective, risk-averse stance. The teenager, conversely, would typically display a greater tolerance for the possibility of such an error due to a greater appetite for risk.

Statistics Part V Test - Inference for Proportions

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