Question

A colleague contacts you regarding the creation of a confidence interval around a mean that is too wide to provide much information. Which of the following options would lead to a smaller interval width?

1) decreasing the sample size

2) increasing the confidence level from 95% to 99%

3) increasing the sample size

4) none of these option would decrease the interval width

Answer 1

Decreasing the sample size and increasing the confidence level would both result in a wider confidence interval. Increasing the sample size is the correct option, as it leads to a narrower confidence interval by reducing the standard error.

Step-by-step explanation:

To determine which option leads to a narrower confidence interval around the mean, let's examine the impact of the options provided:

• Decreasing the sample size generally leads to a wider interval due to increased uncertainty, so this would not accomplish the goal.
• Increasing the confidence level from 95% to 99% would also result in a wider interval because more area is included under the normal distribution curve, representing a larger range of values to capture the true population mean with greater certainty.
• However, increasing the sample size reduces the standard error of the mean and leads to a narrower confidence interval, providing more precise estimates of the population mean.

Therefore, the correct answer is option 3: increasing the sample size leads to a narrower interval width.