For a very large sample size, the ratio between SE_X̄ and σ is 8:40. Determine the sample size n:

Correct option is A

The relationship between the standard error of the mean (SEXˉSE_{\bar{X}}

​SE_X̄) and the population standard deviation ($\sigma$) is given by:​

Information Booster:

The standard error of the mean (SE_X̄) is an important concept in inferential statistics. It quantifies the accuracy of the sample mean (X̄) as an estimate of the population mean (μ\muμ). The formula for SE_X̄ is:

• $\sigma$: Population standard deviation.
• $n$: Sample size.

Key Takeaways:

1. As $n$ increases, SE_X̄SEXˉSE_{\bar{X}}ˉ​ decreases, making the sample mean a more precise estimate of the population mean.
2. SE_X̄ is inversely proportional to √n, meaning the error reduces as the sample size grows.

The ratio provided helps determine the sample size needed for a specific level of precision in estimation.