Final answer:
Decreasing the confidence level from 95% leads to a narrower confidence interval because it equates to less certainty on whether the interval contains the population mean, resulting in a smaller range needed.
Step-by-step explanation:
If a job candidate uses a smaller confidence level than 95% for the average hours of work, the width of the confidence interval would decrease. This is because a confidence interval reflects the range within which we can expect the true population mean to fall with a certain level of confidence. By choosing a smaller confidence level, you are expressing that you require less certainty that the interval contains the population mean, thus the range can be narrower.
For example, if the firm needs at least a 96 percent confidence level, and they want to estimate the average length of time to within one hour, the number of people they need to survey might increase to achieve this more precise estimate. This is due to the fact that a higher confidence level typically requires a larger sample size to maintain the same margin of error.
In comparison, a 99 percent confidence interval is wider than a 95 percent confidence interval because it covers more of the distribution—it has a larger area under the normal curve. When the confidence level is reduced from 99 percent to 90 percent, the error bound will decrease along with the width of the interval as less area is needed under the curve to capture the true mean.