Question

You are performing a hypothesis test of a single population proportion. What must be true about the quantities of $n p$ and $n q$ ?

   You are performing a hypothesis test of a single population proportion. What must be true about the quantities of $n p$ and $n q$ ?

Introductory Business Statistics

Introductory Business Statistics

Alexander Holmes,… 1st Edition

Chapter 9, Problem 29

Instant Answer

Solved by Expert Bryan Meares

09/21/2020

Step 1

First, we know that we are dealing with a single population proportion, which means we have a single population with a proportion of success (p) and a proportion of failure (q). Show more…

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You are performing a hypothesis test of a single population proportion. What must be true about the quantities of $n p$ and $n q$ ?

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Key Concepts

Hypothesis Testing for Proportions

This concept involves testing a claim about a population proportion using sample data. It requires setting up null and alternative hypotheses and then using a test statistic to determine whether to reject the null hypothesis, usually under the assumption that the sample proportion follows an approximate normal distribution.

Success-Failure Condition

When using the normal approximation to the binomial distribution in a proportions test, the expected number of successes (np) and the expected number of failures (nq) must both be sufficiently large, typically at least 10. This condition ensures that the sampling distribution of the proportion is approximately normal, which is a key requirement for the validity of the test.

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