#24 - A certain airport security scanner designed to detect

[Administrator]

Complete Question Explanation

Flaw in the Reasoning. The correct answer choice is (E)

According to the central premise of the argument, if the scanner examines 100 pieces of luggage containing no explosives, it will erroneously “detect” explosives in one piece. A false positive rate of 1% does not, however, guarantee that explosives are present in 99 out of 100 pieces of luggage that trigger an alert. In fact, the premise tells us nothing about what percentage of the alerts are accurate. Picture an airport with tens of thousands of pieces of luggage being scanned daily. What if not a single one of them contained an explosive? According to the premise, if the scanner examines 10,000 pieces of “safe” luggage, it will erroneously detect explosives in 100 of them (false positive rate of 1%). Are explosives present in 99 of these 100 pieces of luggage? Hardly; explosives weren’t present in any of them.

Since the premise deals with the proportion of “safe” pieces of luggage that erroneously trigger an alert, while the conclusion deals with the proportion of alerts that accurately detect an explosive, the premise and the conclusion deal with proportions based on two different groups. Answer choice (E) is therefore correct.

Answer choice (A): The argument only deals with the scanner’s false-positive rate. It need not consider the false-negative rate (i.e. failing to signal an alert when the luggage does contain an explosive) when determining what percentage of the alerts are accurate. This answer choice is incorrect.

Answer choice (B): There is no reason to suspect that the sample is biased, nor is the conclusion about the scanner’s reliability too general. This answer choice is incorrect.

Answer choice (C): How the scanner’s operator reacts to an alert is entirely inconsequential to this argument. The conclusion is only about the proportion of accurate alerts, not about whether the alerts will always trigger an appropriate response on the part of the scanner’s operator. This answer choice is incorrect.

Answer choice (D): Whether some explosives are more easily detectable than others is irrelevant to a conclusion regarding what percentage of the alerts are accurate. The observation introduced in this answer choice can only be used to explain a false-negative rate (i.e. why the scanner fails to signal an alert when the luggage does, in fact, contain an explosive), which is not an issue in this argument. This answer choice is incorrect.

Answer choice (E): This is the correct answer choice. See discussion above.

[Kp13]

hi,

I am having trouble figuring out why exactly choice E is correct. (I picked B). I think it is something to do with the way the author jumps from percentage to numbers. But I can't quite pin-point/articulate the exact flaw.

Thank you for your help.

[Nikki Siclunov]

Hello Kp13,

Thanks for your question. To understand the flaw in the reasoning, let's look at the evidence first: the scanner will erroneously alert the operator for 1% of the luggage that contains no explosives. So, out of 100 bags that have no explosives, the scanner will sound an alarm exactly once, indicating a false positive rate of only 1%. So, the proportion of negatives that are correctly identified as such is 99% (the scanner's specificity rate). FYI, "specificity" measures the proportion of negatives which are correctly identified as such. In our case, 99/100 bags with no explosives were correctly identified as such.

This does not mean, of course, that in 99/100 alerts an explosive will actually be present. Imagine scanning 10,000 bags, none of which containing any explosives. Given a false positive rate of 1%, you should expect that the scanner will sound an alarm 100 times. In none of these alerts will explosives actually be present, contrary to what the conclusion will have you believe. It is impossible to draw the conclusion we want, because we have no information as to how many of the scanned bags will actually have explosives. If all we are testing is clean bags, then of course 100% of the alarms will be false positives.

Let me know if this makes sense

Thanks!

[reop6780]

Here comes my weakness combined with number.

(flaw type with percentage...)


I chose answer A, and the correct answer is E.

I think answer A and E are basically pointing out the same flaw.

(I may still miss the important difference between A and E


The problem occurs when the author calculates the percentage of alarm's accuracy.

As far as I understand, the 1 percent comes from bags without bomb.

XXXXXXXXXXXXXXXXX.

and the 99 percent should apply to the situation where they still think of bags without bomb.


However, the conclusion takes this 99 percent into the situation where bombs are present in the bags.

OOOOOOOOOOOOOOO....

Hence, I agree answer E is correct.

At the same time, I thought answer A should be taken into account to truly explain the alarm's accuracy while my head was getting full of percentage of mixed group

XXXOOOOXOXOXOOOOXX

(percentage of alarm's accuracy)


Anyway, I already expect one possible solution to this problem : "it's OK to ignore such possibility of the scanner's...."

Still, I need further explanation why answer A is incorrect.

(Is this kind of question going to be easier for me once I complete the section of numbers in Question Type Training? )

[Robert Carroll]

reop6780,

Look carefully at what the premise is saying: in 1 out of 100 of the pieces of luggage that contain no explosives, the alert will trigger. So in 99 out of 100 pieces of luggage that contain no explosives, the alert will not trigger. The author erroneously talks about 99 out of 100 alerts, but all we know is that 99 out of 100 pieces of luggage without explosives will NOT alert.

There was only one problem with the alert system that the premises told us about - sometimes, an alert will occur even when a piece of luggage has no explosives. The problem that you saw COULD have been in the stimulus, but which wasn't in there (be careful to note that!), is about an alert NOT happening when a piece of luggage contains explosives. We are told, though, that "A certain airport security scanner designed to detect explosives in luggage will alert the scanner's operator whenever the piece of luggage passing under the scanner contains an explosive." When it does contain an explosive, the alert does happen. So we don't need to worry about that. A is talking about that situation, but the first sentence of the stimulus relieved us of the need to worry about it.

The flaw is in using 1% of one group to talk about 1% or 99% of another group - the percentages are of different groups, so we can't transfer them that way. The stimulus never ignored the possibility of a "false negative", where luggage contains explosives but no alert happens, because the first sentence tells us that the system always alerts on that. The only thing it does wrong is sometimes alerts too often; it never fails to alert when it should. Make sense?

Robert

[reop6780]

It was really confusing problem for me, and thank you for clarifying this one !

[Sherry001]

Hello;
could you please help me understand why A is wrong? I completely understand that the flaw in the argument is the jump from percentage to numbers, I just want to make sure I got rid of A for the right reasons.

1- Certain airport scanner designed to detect explosives will alert the operator.
2- The scanner will erroneously alert the operator for only one percent of the luggages that contain no explosives.

C: Thus, 99 out of 100 alerts of explosives will actually be present.


A) author never ignores this possibility, as she or he clearly states that 99 out of 100 will have.
B)no general conclusion is drawn and no reason for biased study has been done.
C)Human error is irrelevant.
D)equal sensitivity is irrelevant.
E) Yes sir. moves from percentages to numbers.

Thanks so much
Sherry

[Nikki Siclunov]

Hi Sherry,

This is a challenging problem, so let's look at the information in the stimulus more closely:

The information in the stimulus deals with statistical measures of sensitivity and specificity. Specificity (also called the true negative rate, TNR) measures the proportion of negatives that are correctly identified as such (e.g., the percentage of safe luggage that is correctly identified as not having an explosive). Specificity tells us nothing about sensitivity. Sensitivity (also called the true positive rate) measures the proportion of positives that are correctly identified as such (e.g., the percentage of dangerous luggage that is correctly identified as having an explosive). The two concepts are completely unrelated.

According to the central premise of the argument, if the scanner examines 100 pieces of luggage containing no explosives, it will erroneously “detect” explosives in one piece. Thus, the true negative rate is 99%, and the false positive rate is 1%. A false positive rate of 1% does not, however, guarantee that explosives are present in 99 out of 100 pieces of luggage that trigger an alert. In fact, the premise tells us nothing about what percentage of the alerts are accurate. Picture an airport with tens of thousands of pieces of luggage being scanned daily. What if not a single one of them contained an explosive? According to the premise, if the scanner examines 10,000 pieces of “safe” luggage, it will erroneously detect explosives in 100 of them (false positive rate of 1%). Are explosives present in 99 of these 100 pieces of luggage? Hardly; explosives weren’t present in any of them.

Since the premise deals with the proportion of “safe” pieces of luggage that erroneously trigger an alert, while the conclusion deals with the proportion of alerts that accurately detect an explosive, the premise and the conclusion deal with proportions based on two different groups. Answer choice (E) is therefore correct.

Answer choice (A) is incorrect, because the argument only deals with the scanner’s false positive rate. It need not consider the false negative rate (i.e. failing to signal an alert when the luggage does contain an explosive) when determining what percentage of the alerts are accurate. We are only concerned with the scanner's specificity, not its sensitivity.

Answer choice (B) is incorrect, because there is no reason to suspect that the sample is biased, nor is the conclusion about the scanner’s reliability general.

How the scanner’s operator reacts to an alert - answer choice (C) - is entirely inconsequential to this argument. The conclusion is only about the proportion of accurate alerts, not about whether the alerts will always trigger an appropriate response on the part of the scanner’s operator.

Answer choice (D): Whether some explosives are more easily detectable than others is irrelevant to a conclusion regarding what percentage of the alerts are accurate. The observation introduced in this answer choice can only be used to explain a false-negative rate (i.e. why the scanner fails to signal an alert when the luggage does, in fact, contain an explosive), which is not an issue in this argument.

Hope this makes sense! Let me know.

Thanks!

[Johnclem]

Hi powerscore,
This question was particularly difficult for me. I think it's perhaps because everytime I see anything with any sort of numbers, my brain just stops working.

so just to make sure I'm understanding the above explanation percectly... Is the flaw here a "term shift " ? The author concludes in regards to luggages with explosives , when the evidence only discussed non-explosive luggages . So in reality we don't know anything about the proportions of luggages that contain explosives in them.
Did I finally get this ?

Thank you
John

[Adam Tyson]

John,

This one does not have a time shift error - those are errors that are based on the flawed belief that what happened in the past must happen again in the future. For example, every time the Carolina Panthers have made it to the Super Bowl, they have lost. Therefore, if they make it to the Super Bowl again this year, they will surely lose. While that conclusion may indeed be true, the argument isn't sound, because I based it solely on what has happened in the past.

Here, I'm sorry to say, it is just about the numbers and percentages. Your brain reacts the way many others do! There seems to be a high percentage of LSAT-takers who are not what you would call mathematically inclined - we tend to come from more of a liberal arts and humanities background than from STEM education.

Sometimes, though, you just have to run the numbers. How many bags are scanned that have explosives in them? How many that do not? What if they scanned 1000 bags that had no explosives in them, and none that had explosives? 1 percent would falsely alert - that would be 10 alerts, all false, right? That shows that a claim that 99 out of 100 alerts will be the real deal is baloney! The author confused the percentage of false alerts among those bags with no explosives with the percentage of false alerts among all of the alerts. Whoops!

Answer E is worded in a way to cause confusion, and it does that pretty well. However, if you recognize that this is a numbers and percentages flaw, even if you can't quite put your finger on the math to demonstrate the problem, you should be able to zero in on E as being the only answer that addresses that type of error.

When faced with a numbers issue, try supplying some numbers, or at least asking yourself if you have sufficient numerical info to draw a numerical conclusion. Are you comparing two groups whose relative sizes you don't know? Are you looking at one group that is a subset of another, or could they merely overlap or even be completely different? Practice this with many of these questions until it becomes second nature to at least think about the numbers and recognize what you have and what you are missing.

Keep going! You (and your brain) can do it!