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Difficulty: MediumResolving Statistical and Proportional Paradoxes

Over the past decade, the national overall success rate for startups seeking first-round venture capital funding has increased significantly. However, a comprehensive industry analysis reveals that the funding success rate for tech startups has declined over this period, and the funding success rate for non-tech startups has also declined over the exact same period. The analysis classifies every startup seeking funding as either a tech startup or a non-tech startup.

Which one of the following, if true, most helps to resolve the apparent discrepancy described above?

  1. A
    The criteria used by venture capital firms to evaluate non-tech startups have become much more stringent over the past decade than those used for tech startups.
  2. B
    Ten years ago, tech startups and non-tech startups had approximately the same success rate for securing first-round venture capital funding.
  3. Over the past decade, the proportion of all startup funding applications that come from tech startups has grown substantially, and tech startups have consistently had a considerably higher funding success rate than non-tech startups.Answer
  4. D
    The total absolute number of tech startups that successfully secured funding last year was significantly higher than the number of non-tech startups that secured funding.
  5. E
    Over the past decade, the total amount of money invested by venture capital firms has grown much faster than the number of new startups being formed.

Answer

The option stating that the proportion of applications coming from the historically more successful tech sector has grown substantially.
The discrepancy described in the stimulus is a classic example of Simpson's Paradox, where a trend appears in different groups of data but disappears or reverses when these groups are combined. The correct answer provides the necessary mathematical mechanism to resolve this: a compositional shift. By establishing that tech startups have a significantly higher baseline success rate than non-tech startups, and that tech startups now make up a much larger proportion of the total applicant pool, the overall average is pulled upward toward the tech baseline. This shift in the denominator allows the overall success rate to increase even if the individual rates for both subgroups have dropped.

Step-by-Step Solution

1
Identify the two conflicting statistical facts in the stimulus.
Fact 1: The overall funding success rate increased. Fact 2: The success rates for both exhaustive subgroups (tech and non-tech) decreased.
Understanding the exact nature of the contradiction is required to find a logical and mathematical resolution.
2
Determine the mathematical conditions that allow an overall average to increase while all constituent subgroup averages decrease.
This phenomenon can only occur if the composition of the total group shifts heavily toward the subgroup with a naturally higher baseline rate.
Recognizing this statistical concept (Simpson's Paradox) provides the exact blueprint for the correct answer choice.
3
Evaluate the answer choices to find the one that establishes this necessary compositional shift.
The correct option states that tech startups have a higher baseline success rate and now make up a substantially larger proportion of all applications.
This fully satisfies the mathematical requirements to resolve the apparent discrepancy.

Key Concept

Resolving Statistical and Proportional Paradoxes (Simpson's Paradox)
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Topics

Resolving Statistical and Proportional Paradoxes

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