We have calculated a 95% confidence interval for a proportion and would prefer the confidence interval to be more precise, that is narrower. Using the same sample, we can narrow the confidence interval using which of the following?
A) increasing the confidence level
B) decreasing the confidence level
C) It's impossible to narrow the interval without increasing the sample size.
D) unable to answer with the given information
Is B the correct answer?
Yes.
Yes, B is the correct answer. To narrow the confidence interval for a proportion, you need to decrease the confidence level.
A confidence interval is a range of values within which the true population proportion is estimated to lie. The wider the range, the less precise the estimate. The width of the confidence interval is influenced by two factors: the confidence level and the sample size.
By decreasing the confidence level, you are willing to accept a lower level of confidence in your estimate, and this will result in a narrower interval. For example, if you change from a 95% confidence level to a 90% confidence level, the resulting interval will be narrower.
Increasing the confidence level, as option A suggests, will actually widen the confidence interval and make it less precise. Similarly, option C is incorrect because you can also narrow the interval by increasing the sample size, not just by changing the confidence level.
Thus, the correct answer is B) decreasing the confidence level.