Question

A researcher has conducted a survey using a simple random sample of 225 elementary teachers to create a confidence interval to estimate the proportion of elementary teachers favoring the addition of a soda machine to the cafeteria. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 25 teachers instead of 225 elementary teachers. Which of the following statements best describes how the confidence interval is affected?

a) The confidence interval will be wider.
b) The confidence interval will be narrower.
c) The confidence interval remains the same.
d) It is not possible to determine the effect without additional information.

Answer 1

When surveying a smaller random sample of 25 teachers instead of 225, the confidence interval will be wider.

Step-by-step explanation:

When surveying a smaller random sample of 25 teachers instead of 225, the confidence interval will be wider. This is because decreasing the sample size causes the error bound to increase, resulting in a wider confidence interval. The confidence level and the error bound are inversely related, meaning that as the confidence level decreases, the error bound decreases, making the interval narrower.