Question

The confidence interval for the true value increases with increasing confidence level.The statement is right or not. Explain

Answer 1

Answer 2

The statement is correct. As the confidence level increases, the width of the confidence interval also increases.

A confidence interval is a range of values within which we expect the true population parameter to lie with a certain level of confidence. It is typically expressed as a percentage, such as 95% confidence level or 99% confidence level.

When we calculate a confidence interval, we use a sample from the population to estimate the true population parameter. The confidence level represents the probability that the true population parameter falls within the calculated interval. For example, a 95% confidence level means that if we were to take multiple samples from the population and construct confidence intervals for each sample, approximately 95% of those intervals would contain the true population parameter.

To achieve a higher confidence level, we need to widen the interval. This is because a higher confidence level means we want to be more certain that we capture the true parameter, and to do so, we need to allow for a larger range of possible values.

For example, let's say we calculate a 95% confidence interval for a population mean, and it is from 50 to 70. If we want to increase the confidence level to 99%, the interval will become wider, say from 40 to 80. The 99% confidence interval is wider than the 95% interval because we want to be more confident in capturing the true population mean, and this requires a larger range of possible values.

In summary, as the confidence level increases, the confidence interval becomes wider, providing a greater range of values where we expect the true population parameter to lie with a higher degree of confidence.