To increase the precision of a confidence interval while keeping the confidence level the same, the sample size must be:

Increasing the precision of a confidence interval means reducing its width while maintaining the same confidence level. A wider interval indicates more uncertainty about the estimate, while a narrower interval suggests more precision.

To achieve a narrower confidence interval, one must increase the sample size. This is because a larger sample size reduces the standard error of the estimate (the measure of variability). The formula for the confidence interval incorporates this standard error, and as the sample size increases, the standard error decreases. Consequently, the width of the confidence interval narrows, providing a more precise estimate of the population parameter.

The other options do not facilitate increased precision in the context of confidence intervals. Keeping the sample size the same maintains the current variability, while a smaller sample size would only increase variability, resulting in a broader confidence interval. Randomness of the sample is essential for representing the population accurately, but it does not directly influence the precision of the confidence interval in the manner described. Hence, a larger sample size is the only choice that effectively increases the precision of the confidence interval while holding the confidence level constant.