Question

If the Census did another survey, kept the error bound the same, and surveyed only $50$ people instead of $200$, what would happen to the level of confidence? Why?

Short answer

The confidence level decreases.

Step-by-step solution

Given Information

Only $50$people instead of$200$.

Explanation

A tighter confidence interval with a smaller margin of error will arise from a bigger sample size or lower variability. A wider confidence interval with a larger margin of error will arise from a smaller sample size or higher variability.

The level of confidence would decrease because decreasing $n$makes the confidence interval wider