Question

You are performing a hypothesis test of a single population proportion. You find out that $n p$ is less than five. What must you do to be able to perform a valid hypothesis test?

   You are performing a hypothesis test of a single population proportion. You find out that $n p$ is less than five. What must you do to be able to perform a valid hypothesis test?

Introductory Business Statistics

Introductory Business Statistics

Alexander Holmes,… 1st Edition

Chapter 9, Problem 30

Instant Answer

Solved by Expert Bryan Meares

09/21/2020

Step 1

First, recognize that the issue with having $np$ less than 5 is that the normal approximation to the binomial distribution may not be valid, which can lead to inaccurate results in the hypothesis test. Show more…

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You are performing a hypothesis test of a single population proportion. You find out that $n p$ is less than five. What must you do to be able to perform a valid hypothesis test?

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Key Concepts

Normal Approximation Conditions

When performing hypothesis tests for population proportions, one standard method uses the normal approximation to the binomial distribution. This approximation is justified when the expected numbers of successes (n*p) and failures (n*(1-p)) are both sufficiently large, commonly with a threshold of at least five. If these conditions are not met, the sampling distribution of the proportion cannot be reliably approximated by a normal distribution.

Alternative Testing Methods

If the normal approximation conditions are not satisfied due to a small sample size or low expected count (n*p < 5), it becomes necessary to use an exact testing method. In such cases, methods like the exact binomial test are employed because they rely on the exact probabilities derived from the binomial distribution, thereby providing valid inference without depending on large-sample approximations.

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