College

We appreciate your visit to What is the purpose of checking the Large Counts condition when performing a one sample z test for p A To make sure the population. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

What is the purpose of checking the Large Counts condition when performing a one-sample z test for p?

A. To make sure the population is approximately Normal.
B. To make sure the sample is approximately Normal.
C. To make sure that the sampling distribution of p is approximately Normal.
D. To make sure the observations are close to independent.
E. To make sure that we can generalize the results to a larger population.

Answer :

To perform a one-sample z test for a proportion, the Large Counts condition requires that the numbers [tex]$np$[/tex] and [tex]$n(1-p)$[/tex] are both sufficiently large (usually at least 10). This condition ensures that the sampling distribution of the sample proportion is approximately Normal. In other words, it is used to verify that the use of the Normal approximation (via the Central Limit Theorem) is valid for the proportion.

Thus, the purpose of checking the Large Counts condition is to ensure that

[tex]$$
\text{the sampling distribution of } p \text{ is approximately Normal},
$$[/tex]

which corresponds to option (c).

Thanks for taking the time to read What is the purpose of checking the Large Counts condition when performing a one sample z test for p A To make sure the population. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada