Biostatistics: sample size for a prevalence survey: practice question

A PSM question in the style of the NEET PG paper. Answer it first, then read why the right option is right and why each of the others is wrong.

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PSM · Biostatistics: sample size for a prevalence survey

Sample item

A district team plans a survey of anaemia, expecting a prevalence of 20%. They want an absolute precision of 5% at 95% confidence (taking Z as 2). Using n = 4pq/d squared, what is the required sample size?

Original practice item, not a recalled exam question. Nothing here is recorded.

The answer and the reasoning

C. 256

With p = 20, q = 80 and absolute error d = 5, n = 4 x 20 x 80 / 25 = 6400/25 = 256. Sample size rises when the expected prevalence is closer to 50% and when the desired precision is tighter. Using 5% relative precision (d = 1) would instead give 6400.

Option by option

  • A. 64

    This corresponds to d = 10, which is a looser precision than the one specified.

  • B. 6400

    This results from using relative precision of 5% of 20 (d = 1), not an absolute error of 5%.

  • C. 256 (correct)

    Correct. 4 x 20 x 80 / 5 squared = 256.

  • D. 1024

    This corresponds to d = 2.5, which is a tighter precision than the one specified.

Source note: Original NextPrep sample item — pending expert review. This item is original practice material awaiting independent expert review, so confirm important facts in a standard textbook.

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Questions about this PSM question

What is the answer to this PSM question?

The best answer is C, 256. With p = 20, q = 80 and absolute error d = 5, n = 4 x 20 x 80 / 25 = 6400/25 = 256.

Why is "64" not the answer?

This corresponds to d = 10, which is a looser precision than the one specified.

Why is "6400" not the answer?

This results from using relative precision of 5% of 20 (d = 1), not an absolute error of 5%.

Why is "1024" not the answer?

This corresponds to d = 2.5, which is a tighter precision than the one specified.

What concept does this question test?

It tests Biostatistics: sample size for a prevalence survey in PSM. Sample size rises when the expected prevalence is closer to 50% and when the desired precision is tighter. Using 5% relative precision (d = 1) would instead give 6400.

How hard is this question?

We tag it as a multi-step question: it asks you to combine more than one idea. The tag is our own editorial judgement, not an official difficulty rating, so read the reason for every option, not only the answer.

How should I study Biostatistics: sample size for a prevalence survey?

Practise biostatistics with small calculations until sensitivity, predictive values and risk measures are automatic. Then use the flashcards and the other PSM questions on this site to test what stuck.

Is this a real NEET PG question?

No. It is an original practice item (editorial status: sample, version 1). NextPrep does not publish recalled or leaked questions, and independent faculty review of this item has not been completed yet, so confirm important facts in a standard textbook.