How to find the 10 percent condition of a sample size of 42 and probability of 0.29.
Understand the Problem
The question is asking how to establish the 10 percent condition in the context of a statistical sample with a known size and probability. The 10 percent condition generally refers to ensuring that the population size is at least ten times larger than the sample size to justify certain statistical methods, such as using the normal approximation for a binomial distribution.
Answer
The condition is established by ensuring $N \geq 10n$.
Answer for screen readers
The answer depends on whether the condition $N \geq 10n$ is satisfied, where $N$ is the population size and $n$ is the sample size.
Steps to Solve
- Identify Sample and Population Sizes
First, determine the size of the sample ($n$) and the size of the population ($N$). For the 10 percent condition to hold, we need to check whether the population size is at least ten times larger than the sample size.
- Formulate the Condition
Set up the inequality that needs to be satisfied. The condition can be expressed mathematically as:
$$ N \geq 10n $$
This means the population size ($N$) should be greater than or equal to ten times the sample size ($n$).
- Check Values Against Condition
Substitute the known values of $n$ and $N$ into the inequality and verify if the condition holds true.
- Conclusion Based on Verification
If the condition $N \geq 10n$ is satisfied, you can proceed with the normal approximation methods. If not, consider alternative approaches.
The answer depends on whether the condition $N \geq 10n$ is satisfied, where $N$ is the population size and $n$ is the sample size.
More Information
The 10 percent condition is crucial in statistics as it helps maintain the independence of observations in a sample. If the sample is too large relative to the population, the sample may not accurately reflect the population, inflating the chance of errors in estimation.
Tips
One common mistake is neglecting to compare the absolute sizes of the sample and the population. Ensure that you are looking at the exact values and performing the inequality check correctly.
AI-generated content may contain errors. Please verify critical information
