Question

In interval estimation, as the sample size becomes larger, the interval estimate ________?

1) becomes narrower
2) becomes wider
3) remains the same
4) cannot be determined

Answer 1

As the sample size increases in interval estimation, the interval estimate becomes narrower.

Thus, the correct option is 1.

Step-by-step explanation:

In interval estimation, as the sample size becomes larger, the interval estimate becomes narrower. This occurs because a larger sample size reduces the error bound or error margin.

Essentially, a larger sample provides more information about the population, thereby decreasing the variability and making the estimate of the population parameter more precise. This is why we observe narrower intervals with increasing sample sizes; less variability in the sample mean leads to more confidence that the interval captured is closer to the actual population mean.

Decreasing the sample size, on the other hand, would increase the error bound, leading to a wider interval estimate. It's important to note that the confidence level also affects the width of the interval. If the confidence level is increased, the interval will widen correspondingly because a higher confidence level means that a larger portion of the sample distribution must be covered to ensure the true population mean falls within that range.

Therefore, the correct option is 1) becomes narrower