G3 SEC English, Mathematics and Science | Learner’s Guide Vol 0147. “Not detected” is not always “exactly zero”. Read the test method, reporting threshold and reference group before calculating or making a claim.
A sensor, a survey and a passage can all seem to say “nothing”. This original EMS workshop teaches how to distinguish an observed zero, a rounded zero, a bound and a missing value, with clear examples and complete practice answers.
Chapter index
- 1. A quiet instrument is not proof that nothing happened
- 2. How the 2027 SEC subjects support this shared skill
- 3. Four different statements that look like zero
- 4. A reporting threshold is a rule about the method
- 5. Write bounds rather than make up a point value
- 6. Rounding to zero is not the same as an undetected signal
- 7. In English, a negative statement still has a subject and scope
- 8. In Science, a negative test needs controls and conditions
- 9. Compare tests with different detection limits carefully
- 10. A table with blank cells, dashes and zeros
- 11. A complete interval calculation with one non-detection
- 12. Upper bounds, lower bounds and decisions
- 13. Do not divide by a value that might be zero
- 14. When is an exact zero legitimately useful?
- 15. Source independence: three reports of the same test
- 16. One integrated example: a school garden report
- 17. Common wording traps in exam questions
- 18. Thirty original non-detection and threshold exercises
- 19. An answer clinic: three different kinds of mistake
- 20. Seven days of careful EMS evidence practice
- 21. A clear conclusion carries its evidence with it
- 22. Thirty-two original questions and worked answers
1. A quiet instrument is not proof that nothing happened
Imagine a measuring instrument that can report readings down to 0.2 arbitrary units. A sample is tested, and the screen shows “below 0.2”. One pupil writes that the measured substance is completely absent. Another writes that the amount is 0.2. Both answers claim more than the display actually supplies. The instrument has identified a region of uncertainty, not one exact value.
This is a surprisingly useful skill across G3 SEC English, Mathematics and Science. A passage can describe a sound that was not heard, a table can suppress very small numbers, and an investigation can report “not detected”. The words look like absence, but the evidence may mean only that a result did not cross the test’s reporting threshold.
Learner’s Guide Vol 0147 teaches you to keep three things separate: the thing being measured, the instrument or rule used to observe it, and the conclusion permitted by the result. We will build from plain-language interpretation to inequalities, interval reasoning, fair comparisons and scientific tests. We will also practise recognising the special case where an actual counted zero is meaningful.
The aim is not to be sceptical of every observation. It is to be precise about the strength and reach of evidence. “Not detected by this method under these conditions” is an informative statement. “Nothing exists anywhere” is much stronger and may not follow from it.
2. How the 2027 SEC subjects support this shared skill
The official SEAB 2027 G3 syllabuses list K300 English Language, K310 Mathematics, and several Science routes including K326 Physics/Chemistry, K327 Physics/Biology and K328 Chemistry/Biology. Pure Sciences have separate codes. This guide is a shared reasoning workshop, not a new examination component called “EMS detection limits”.
The K300 English syllabus assesses literal, inferential and evaluative comprehension, accurate vocabulary in context, and synthesis from texts. Reading “not detected” or “none reported” without converting it into an unjustified absolute claim is a language-and-evidence skill. K300 Paper 2 Comprehension lasts one hour and fifty minutes and contributes 35 percent.
The K310 Mathematics syllabus includes equations, inequalities, statistics, measurement and mathematical reasoning. If a number is only known to be less than a positive limit, an inequality or interval may be more accurate than an invented exact value. K310 has two papers of two hours and fifteen minutes each, 90 marks apiece and equal weighting.
The G3 combined Science syllabus explicitly values measurement, its limitations, interpreting observations, handling data, and evaluating investigations. A result that a method could not detect can be meaningful evidence when interpreted within the method’s limits. It need not mean literal absence. The skill is useful across experimental contexts; this article does not claim the syllabus names a separate “detection-limit” chapter.
3. Four different statements that look like zero
“The tally was zero” can describe an exact observed count. “The display rounded to 0.0” describes a representation produced by rounding. “Below 0.2” gives a bound. “No result recorded” may describe missing data rather than any measurement at all. They look similar in a spreadsheet but have different logical meanings.
Suppose a class counts pupils who chose a particular answer and finds none among the 20 participating pupils. An observed zero describes the sample’s count. The result is not an instrument threshold, and it does not prove that nobody in the entire school would choose that answer. Scope still matters.
If a sensor displays 0.0 after rounding to one decimal place, it may have measured a small nonzero value before rounding. If another sensor displays “below detection threshold”, it may not provide a numerical estimate at all. If a cell is blank because the equipment failed, it provides no legitimate value to average without further rules.
Before calculating or explaining, translate the notation into a sentence about what is known. “Exactly zero were counted here”, “the rounded display is zero”, “the quantity lies below a reporting bound”, and “the quantity is unknown because no valid reading exists” are four different claims.
4. A reporting threshold is a rule about the method
A detection threshold is related to the smallest signal a method can distinguish or report under specified conditions. Its precise technical definition depends on the method. For our school-level examples, we will use a simplified reporting rule: signals below a stated positive limit are labelled “below the limit” rather than given an exact numerical value.
Suppose the laboratory’s simplified rule labels any nonnegative concentration under 0.5 mg/L as “below 0.5 mg/L”. The report tells you that the value is within an interval beginning at zero and ending below 0.5 mg/L, assuming the reporting method and units are valid. It does not say whether the true value is 0, 0.1 or 0.49 mg/L.
The threshold is not necessarily a biological, environmental or legal safety boundary. A device being unable to distinguish a small signal does not establish whether that level is harmless or harmful. Those decisions would require a separate criterion and more information. Keep the measurement rule separate from a judgement about consequences.
A student who writes “below 0.5 therefore safe” has skipped an entire logical step. A good exam explanation asks what the limit measures, who defined it, and what further standard or comparison the question actually provides.
5. Write bounds rather than make up a point value
If a quantity x is known to be nonnegative and the result is reported as less than 0.5, write 0 ≤ x < 0.5. The less-than symbol is strict: 0.5 itself is not included. If the report says at most 0.5, the upper bound becomes inclusive: 0 ≤ x ≤ 0.5.
This interval contains many possible values. A reader should not quietly replace it with x = 0 or x = 0.5. The midpoint, 0.25, is not an observed value either; it would be an extra modelling choice requiring justification. A precise response carries the uncertainty forward.
For count data, the interval may contain only whole-number possibilities. If “fewer than five pupils” describes a count, the possible nonnegative integers are 0, 1, 2, 3 and 4. If “at most five” is used, 5 is also possible. Reading the inequality correctly can change whether a proposed plan meets a threshold.
The earlier Vol 0131 inequality workshop teaches the general algebra of inequalities and sign reversal. This volume applies the language of bounds to a specific evidence problem: a result not given as one exact reading.
6. Rounding to zero is not the same as an undetected signal
A value displayed as 0.0 after rounding to one decimal place can represent a range of underlying numbers around zero. Under a conventional nearest-tenth rule and ignoring tie-handling details, values with magnitude below about 0.05 may round to 0.0. If the measured quantity cannot be negative, the plausible interval can be narrowed to nonnegative values.
But a “below 0.1” result usually describes a reporting or detection rule, not ordinary rounding. The limit need not equal the calculator’s rounding precision. A measurement can be displayed with several decimal places while the method itself lacks the ability to distinguish signals below a separate threshold.
An exact count of zero events is different again. If a student honestly tallied zero responses in a defined sample, the count is exact for that recorded sample. We still must ask whether the sample was complete, whether everyone was observed and how far the result can be generalised.
Name the source of the zero-like statement: counting, rounding, non-detection, or missing measurement. Each demands a different calculation and a different degree of confidence.
7. In English, a negative statement still has a subject and scope
“No sound was heard” is not identical to “There was no sound”. The first describes what listeners perceived; the second asserts absence more broadly. A comprehension passage may deliberately keep the distinction open, particularly when a character is far away, distracted or listening through a closed door.
A school announcement might state, “No faults were reported during the morning checks.” This establishes that no faults were reported in that period through the stated process. It does not automatically establish that no faults existed or will ever exist. Reporting is an activity; underlying condition is another matter.
Words such as “detected”, “observed”, “recorded”, “reported”, “tested” and “noticed” contain information about an observer or procedure. Removing the verb in a paraphrase can accidentally turn a narrow claim into an absolute one. Preserve whose observation was involved and when it was made.
A concise examination response can say: “The statement indicates that the test did not identify the signal; it does not prove the signal was absent.” That is clearer than an elaborate guess about why the test was negative.
8. In Science, a negative test needs controls and conditions
A scientific test may return a negative result for several reasons. The target quantity may truly be absent. It may be present below the method’s reporting limit. The sample may have been handled incorrectly, a reagent may not have worked as intended, or interfering conditions may have affected the response. Not all these alternatives are equally likely in every experiment.
The correct conclusion depends on what the test is designed to detect and how its validity was checked. A known positive control can help show that the test procedure is capable of producing the expected response under suitable conditions. A negative control can help reveal unwanted background responses. Those controls address different potential errors.
If a well-controlled test does not detect the target, that still provides useful evidence. It may support a practical conclusion within the method’s stated sensitivity and context. The point is not to say “we can never know anything”; the point is to state what the evidence actually excludes and what remains possible.
A negative result is often most helpful when paired with a clear reporting limit and an appropriate follow-up test. When the question supplies no such details, avoid inventing them.
9. Compare tests with different detection limits carefully
Suppose Method A reports values down to 0.5 units while Method B reports down to 0.05 units under comparable conditions. Method B can, in this simplified example, report smaller signals. But that does not automatically make it the better method for every job. Accuracy, specificity, cost, range, interference and practical suitability also matter.
If A reports “below 0.5” and B reports a value of 0.2 for the same comparable sample, the results can both be true. Method A’s threshold is too high to report a precise 0.2 value, while B can provide one. The measurements do not necessarily contradict each other.
If both methods report “below limit”, you need to know their respective limits before comparing what has been ruled out. “Below 0.5” leaves a wider interval than “below 0.05” for a nonnegative quantity. Their verbal similarity hides a real difference in numerical information.
When a question asks which result is more informative, discuss the specific range that each method can distinguish, not just the number of decimal places printed on the report.
10. A table with blank cells, dashes and zeros
Imagine a table with five columns: sample name, test result, unit, test method and notes. One row contains “0”, one contains “<0.2”, one contains a dash, and one contains “not applicable”. It would be a mistake to treat all four as zeros when calculating a mean.
A dash may mean not measured, not recorded, withheld or another legend-defined category. “Not applicable” may mean the question does not make sense for that observation. Neither provides a numerical value just because the cell is not filled with a large positive number.
A careful analyst reads the legend or methods note. If it says a dash means “missing instrument reading”, that row cannot be interpreted as a true zero. If the exercise asks for a mean over valid measurements only, determine which rows qualify. The denominator depends on that decision.
The ability to maintain data ownership is not confined to spreadsheet work. In English, a table’s heading and footnote can qualify every number below it. In Science, experimental conditions can limit comparison. In Mathematics, treating a blank cell as zero can corrupt a total and its subsequent percentage.
11. A complete interval calculation with one non-detection
Suppose three equal-duration readings represent nonnegative amounts of material, in grams. The first is exactly 1.2 g, the second is exactly 0.8 g, and the third is reported as “below 0.5 g”. The third reading is not an observed zero, and it is not 0.5 g. For this simplified exercise, call it x with 0 ≤ x < 0.5.
The combined mass is 1.2 + 0.8 + x, so it lies between 2.0 g inclusive and 2.5 g exclusive. If the question requests the mean amount across the three readings, divide the entire interval by 3: the mean lies from 2/3 g inclusive to 5/6 g exclusive, about 0.667 g up to but not including 0.833 g.
Reporting the mean as exactly 0.667 g would assume the third reading was zero. Reporting exactly 0.833 g would assume it was at the upper bound and would even violate the strict inequality. An interval is the mathematically faithful result when no additional measurement is given.
If a practical question requires a single numerical estimate, it must provide or justify an estimation rule. Without that, do not invent one. An accurate bound can be a stronger mathematical answer than an unsupported decimal.
12. Upper bounds, lower bounds and decisions
Suppose a competition rule allows at most 12 entries. A school has confirmed 10 entries and says “fewer than three additional entries are expected”. If entries are whole numbers and nonnegative, the additional count could be 0, 1 or 2. The largest possible total is 12, so the reported bound is consistent with the stated limit.
Now change the sentence to “three or fewer additional entries”. That includes three, so the total could reach 13 and breach the rule. Only one word has changed, but the decision changes with it. Reading the bound is part of understanding the task.
A similar pattern occurs when a measured value is reported below a threshold. If the decision rule is “strictly less than 0.5”, a valid report of “<0.5” supports the comparison. If the decision rule requires proof of an exact zero, the same report does not meet that much stronger requirement.
Always keep the decision threshold separate from the measurement threshold. One is a rule about what counts as acceptable; the other is a statement about what the method can report. They may coincide in a question, but you cannot assume that they do.
13. Do not divide by a value that might be zero
A percentage change is normally calculated relative to an original nonzero amount. If the original measured quantity is simply reported as “below 0.2” and may be zero, a percentage increase from that value may be undefined or highly uncertain. You cannot quietly replace the original with 0.2 and produce a neat percentage.
For example, a later sensor reading of 0.4 after an earlier “below 0.2” result tells you the later measured value exceeds the earlier bound under comparable reporting conditions. The absolute increase is greater than 0.2 units if the earlier nonnegative quantity was strictly below 0.2. But an exact percentage change is not supported by the earlier report.
If the earlier true value were zero, the ordinary percentage-change denominator would be zero. If the value were 0.1, the percentage increase would be different from what it would be at 0.01. Both may fit the earlier bound. A single reported percentage would invent information.
The Vol 0125 zero-denominator workshop owns the arithmetic problem of division by zero. This guide owns the earlier evidence decision: a reading below detection should not be substituted with an unjustified number that hides or creates a denominator problem.
14. When is an exact zero legitimately useful?
A class observes a feeder for ten minutes and counts zero birds landing during that interval. The tally legitimately reports no landings observed in that place and time. The observation does not establish that there were no birds nearby or that no birds visited before or after the interval.
An inventory can contain exactly zero red folders at the moment of counting if all items were inspected and categorised correctly. That is stronger evidence about the defined inventory than a sensor displaying “below threshold” is about an unobservable trace quantity. But any later stock change would require a new count.
Some mathematical problems define zero exactly through a relationship: x = 0 satisfies an equation or the zero point marks an origin. That is a formal property in the mathematical model, not the same thing as a laboratory device reporting an undetected quantity.
Precision comes from knowing how the zero was obtained and the scope to which it applies. Avoid the opposite error of refusing every zero. A carefully defined exact zero is informative; a rounded zero or nondetection statement is informative in a different way.
15. Source independence: three reports of the same test
Imagine three websites say a chemical was not detected in a river sample. If all three refer to the same original laboratory report, the repetition does not create three independent tests. There may be one observation published in three places.
The later articles may have useful commentary, but they do not automatically make the laboratory result more precise or lower the original method’s detection threshold. A source cannot acquire new measuring power through repetition. Read the original reported value, method and sample conditions if available.
A genuinely independent measurement may add evidence, particularly if it uses a validated method with suitable sensitivity. But even then, check whether the samples represent the same place, time and target quantity before calling the results directly comparable.
The earlier Vol 0133 source-independence workshop addresses evidence that is repeated across publications. The present volume adds the distinct measurement-limit question: what did the underlying test itself actually establish?
16. One integrated example: a school garden report
A school prepares a fictional garden-monitoring report. A simple sensor records soil-moisture readings of 12 units, 8 units, and “below 2 units” on three separate days. A pupil writes, “The soil had no moisture on day three.” The third reading does not justify that conclusion; it only indicates the instrument could not report a value at or above its stated threshold under the measurement rule.
In Mathematics, the day-three value x can be represented as 0 ≤ x < 2, assuming moisture is represented by a nonnegative amount. The decrease from day two is 8 − x, so it is greater than 6 and at most 8 units. That interval carries the measurement uncertainty into the comparison instead of replacing it with an exact guess.
In English, a source-faithful report might state, “The sensor reading fell below its reporting limit on day three, after showing 8 units on day two.” In Science, a follow-up might use a suitable instrument with a lower reporting threshold or inspect calibration and environmental conditions to obtain more informative measurements.
This is not an official SEC question. It demonstrates how one observed result can support different kinds of careful work without changing its underlying meaning. A valid mathematical inequality and a clear English sentence should agree about what was and was not measured.
17. Common wording traps in exam questions
“Not detected” is about a method and its conditions. “Not present” is about the underlying thing. “No response recorded” can describe missing recording. “Zero respondents selected this choice” is a count for a particular survey. These statements should not be exchanged simply because they all look like a kind of absence.
“At most” includes the limit; “less than” does not. “No more than 5” usually corresponds to ≤5; “fewer than 5” corresponds to <5 for a count. “Below the lowest measurement” may be a bound rather than a known true zero.
Question wording sometimes gives a reporting convention such as “All values under 0.1 are shown as 0”. In that case, a printed zero is coded according to the stated rule. Read the convention before treating it as an exact quantity.
A quick answer audit asks: What was measured or counted? What was the instrument or reporting rule? What exact interval or count follows? How far can the written conclusion extend? Keeping those four answers visible prevents an apparently small wording error from becoming a large unsupported inference.
18. Thirty original non-detection and threshold exercises
These original examples combine short comprehension claims, mathematical bounds and experimental interpretation. They are intentionally not all numerical. You will need to say when a result is unknown, when zero is a legitimate count and when a measurement gives an interval rather than one value.
Before inspecting each solution, write the strongest claim supported by the evidence, but no stronger. If you choose an interval, include whether the endpoints belong to it. If you describe a test, mention its method or threshold rather than turning “not detected” into “does not exist”.
The school-level focus is on disciplined reading and reasoning. Detailed analytical laboratory detection theory is not required to use these examples. Our simplified threshold rules are stated inside the questions so you can work entirely from the information supplied.
19. An answer clinic: three different kinds of mistake
The first mistake is an unsupported point estimate: setting x = 0.2 when the instrument says x < 0.2. Repair it by writing an inequality. The second mistake is scope inflation: claiming that nobody anywhere chose an option because zero people in a small survey did. Repair it by naming the surveyed group and measurement period.
The third mistake is method confusion: using a rounded zero, a failed reading and a below-threshold result as if they were interchangeable. Repair it by reading the table legend or measurement note before doing any arithmetic. A small notation difference may change whether a number can legitimately be used in a mean or percentage.
Different errors need different practice. More arithmetic will not by itself repair a misunderstood scientific test; more vocabulary drills will not repair an incorrectly reversed inequality. Diagnose the first unsupported step and practise one contrasting example.
A learner who can say why an attractive exact answer is unjustified is already showing advanced examination judgement. Accuracy includes knowing when the provided evidence supports only a range or qualified statement.
20. Seven days of careful EMS evidence practice
Day one: classify statements as exact zero, rounded zero, below threshold or missing reading. Day two: write inequalities from less than, at most and nonnegative bounded observations. Day three: solve simple total and mean intervals when one value is reported below a limit.
Day four: compare two tests with different reporting limits and explain when their findings can both be valid. Day five: practise English paraphrases that preserve “observed”, “reported” and “detected” rather than deleting those qualifiers. Day six: answer mixed tasks involving a survey, a sensor and a Science investigation.
Day seven: review actual mistakes and make three new examples that differ from the ones you memorised. A tutor can ask “Did you measure zero, or could you not measure below the limit?” A parent can ask “Does this conclusion describe the sample or everybody?” Those calm questions help the learner discover the reasoning rather than borrow an answer.
The point is not to turn every school question into a philosophical debate. Most well-specified items have a workable answer. You want a short routine that keeps the answer inside the evidence and then allows you to move on confidently.
21. A clear conclusion carries its evidence with it
A useful answer distinguishes a process from the result reported by that process. Instruments have limits, surveys have samples, written reports have scopes, and mathematical symbols have exact meanings. Ignoring one of those limits can make a sentence or calculation sound more certain than the evidence allows.
Follow the G3 SEC Learner Guide and Examination Craft hub for the wider preparation route. Secondary English, Mathematics and Science provide their distinct foundations, and the PSLE Learning Guide remains useful when sample, measurement and basic reading skills need rebuilding.
This volume should leave one habit: whenever you read “nothing”, “zero”, “not detected” or “below”, ask what the original observation truly was. State that clearly, preserve any numerical bound and explain only what follows. That is how careful interpretation becomes reliable examination performance.
22. Thirty-two original questions and worked answers
Try each exercise using only the reporting rule or statement provided. The answer that sounds most certain is not automatically the answer justified by the evidence. The original cases below include sample conclusions, sensor bounds and numerical intervals.
Question 1. A sensor reports <0.2 units for a nonnegative quantity x. What is known?
Worked answer. 0 ≤ x < 0.2.
Reason. The true value is bounded, not specified as exactly zero.
Question 2. Does “below 0.2” mean exactly 0.2?
Worked answer. No.
Reason. The strict threshold excludes 0.2.
Question 3. Can x = 0 be possible under 0 ≤ x < 0.2?
Worked answer. Yes.
Reason. Zero may be possible but is not proved.
Question 4. What if the report says at most 0.2?
Worked answer. 0 ≤ x ≤ 0.2, if x is nonnegative.
Reason. The upper boundary is inclusive.
Question 5. Fewer than five pupils arrive. List nonnegative whole-number possibilities.
Worked answer. 0, 1, 2, 3, 4.
Reason. The phrase excludes 5.
Question 6. At most five pupils arrive. Is five allowed?
Worked answer. Yes.
Reason. At most includes the stated maximum.
Question 7. A survey receives zero votes for a choice from its 20 respondents. Can we say no one in the school prefers it?
Worked answer. No.
Reason. The count belongs to the 20 respondents, not the whole school.
Question 8. A device displays 0.0 after rounding. Must the underlying value be exactly zero?
Worked answer. No.
Reason. A small nonzero value can round to zero.
Question 9. A blank cell represents a failed sensor. Can it be entered as 0 in a mean?
Worked answer. Not without an explicit, justified data rule.
Reason. Missing measurement is not an observed zero.
Question 10. A result says “not applicable”. Is it the same as zero?
Worked answer. No.
Reason. The question or quantity may not apply to that case.
Question 11. Two methods have limits 0.5 and 0.05. Which reports smaller signals in the simplified model?
Worked answer. The method with limit 0.05.
Reason. Its numerical reporting threshold is lower, assuming otherwise comparable methods.
Question 12. Method A says <0.5; Method B reports 0.2. Must they contradict each other?
Worked answer. No.
Reason. The 0.2 value fits below Method A’s threshold.
Question 13. A test is negative. Does this always prove a substance is absent?
Worked answer. No.
Reason. It may be absent, below detection, or affected by test conditions.
Question 14. What can a positive control help establish?
Worked answer. That the test can show its expected positive response under suitable conditions.
Reason. It does not necessarily solve every possible sampling or interference issue.
Question 15. What can a negative control help reveal?
Worked answer. Unexpected background responses or contamination under the test design.
Reason. Controls serve different interpretive roles.
Question 16. A report says “no faults were reported”. Is that equivalent to no faults existed?
Worked answer. No.
Reason. Reporting and the underlying condition are different.
Question 17. A person did not hear a sound. Does that prove no sound occurred?
Worked answer. No.
Reason. Detection depends on the listener, distance and conditions.
Question 18. Amounts are 1.2 g, 0.8 g and x with 0 ≤ x < 0.5. Bound their total.
Worked answer. 2.0 ≤ total < 2.5 g.
Reason. Add the known amounts and propagate the interval.
Question 19. For those three amounts, bound the mean.
Worked answer. 2/3 ≤ mean < 5/6 g.
Reason. Divide both total bounds by three.
Question 20. Can the third amount simply be entered as 0.5 g?
Worked answer. No.
Reason. The strict report says it is below 0.5.
Question 21. Can the third amount simply be entered as 0 g?
Worked answer. Not without an additional justified convention.
Reason. Zero is one possibility, not the observed result.
Question 22. An earlier reading is <0.2 and later reading is 0.4. Is exact percentage change known?
Worked answer. No.
Reason. The earlier denominator is uncertain and could be zero.
Question 23. What absolute increase can be inferred if earlier x is nonnegative and <0.2 and later is 0.4?
Worked answer. The increase is >0.2 and ≤0.4 units.
Reason. Subtract an unknown value in [0,0.2) from 0.4.
Question 24. A school has 10 confirmed entries and fewer than 3 more. What is maximum?
Worked answer. 12 entries.
Reason. The additional nonnegative integer maximum is 2.
Question 25. If instead 3 or fewer more may arrive, can total exceed 12?
Worked answer. Yes, it can reach 13.
Reason. The boundary is now inclusive of 3.
Question 26. Three websites repeat one laboratory result. How many original tests does this necessarily provide?
Worked answer. Only one original test is established.
Reason. Copies are not independent measurements.
Question 27. A measured value is below the instrument limit. Does that alone prove it is safe?
Worked answer. No.
Reason. Measurement and a safety criterion are different pieces of information.
Question 28. A birdwatcher records zero landings in ten minutes. What can be concluded?
Worked answer. No landings were recorded in that monitored period and place.
Reason. It does not establish that no birds exist nearby.
Question 29. A simplified rule prints 0 whenever a value is below 0.1. Is a printed 0 necessarily exact?
Worked answer. No.
Reason. The reporting convention encodes a range.
Question 30. A school sensor changes from 8 to <2. How much did it decrease?
Worked answer. By more than 6 and at most 8 units, assuming nonnegative readings.
Reason. Subtract x in [0,2) from the earlier 8.
Question 31. What is stronger: “not detected by this test” or “does not exist”?
Worked answer. “Does not exist” is a much broader claim.
Reason. The test result alone need not establish absence.
Question 32. When does a below-threshold report support a strict numerical decision?
Worked answer. When the stated valid bound is directly sufficient for the decision’s threshold.
Reason. Do not confuse the instrument’s limit with a separate decision or safety standard.
