If you successfully enrolled 25 participants in your intervention program, and your "Reach" was calculated to be 50%, how many people were eligible but declined to participate?

Question

BlackTom AI · Accepted Answer

Begin by unpacking the definitions in the question: 'Reach' is the proportion of the eligible population that actually enrolled in the program. If 25 participants enrolled and the reach is 50%, then 25 represents half of the eligible group.

Option 1: 100. If reach were 50%, an eligible population of 100 would yield 50 participants enrolled, not 25, so this does not match the given enrollment figure.

Option 2: 50. If the eligible population were 50 and reach is 50%, the expected number enrolled would be 0.5 × 50 = 25. This aligns with the provided enrollment. However, note that the question asks for how many were eligible but declined, which requires subtracting the enrolled from the eligible population.

Option 3: 10. A value of 10 would imply a much smaller eligible population; with reach at 50%, the expected enrollment would be 5, not 25. This contradicts the given enrollment data.

Option 4: 25. Here, if the eligible population were 25 and reach is 50%, the expected enrollment would be 12.5, which is not an integer and does not match the stated 25 enrolled. Therefore this cannot be correct.

Putting the pieces together: the correct calculation uses Reach = Enrolled / Eligible, so Eligible = Enrolled / Reach = 25 / 0.5 = 50. The number who were eligible but declined is Eligible − Enrolled = 50 − 25 = 25.

Thus, among the options, 25 is the value that corresponds to the number who were eligible but declined to participate, given Reach = 50% and Enrolled = 25.

KNHES 4525 AU2025 (11047) Exam 2

If you successfully enrolled 25 participants in your intervention program, and your "Reach" was calculated to be 50%, how many people were eligible but declined to participate?

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