Question
The population proportion is assumed to be 0.16 . If the desired standard error is 0.0127 or less, what is the minimum sample size
needed?
needed?
Ask by Henry Norris. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The minimum sample size needed is 834.
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
Beyond the Answer
To determine the minimum sample size needed for a population proportion of 0.16 with a desired standard error of 0.0127 or less, you can use the formula for the standard error of proportion:
Where
is the standard error,
is the population proportion, and
is the sample size. Setting
to 0.0127 and
to 0.16, you need to solve for
:
- Plug in the values:
- Square both sides:
- Rearranging gives you:
- Calculate:
Since sample size must be a whole number, round up to 834. Thus, the minimum sample size needed is 834.
So if you’re planning to conduct a survey or an experiment based on this population proportion, make sure to gather a sample of at least 834 individuals to achieve your desired level of precision!