95% Confidence Interval

E

Note that III is incorrect since the confidence interval is a range estimate and hence, cannot represent a point estimate of the population parameter itself.

A confidence interval is a range of values within which we believe the true population parameter lies. It provides a measure of uncertainty around our estimate. The level of confidence associated with a confidence interval indicates the probability that the interval contains the true population parameter.

I. 95% of similarly constructed intervals will contain the population parameter. This statement is true. When we construct a 95% confidence interval, it means that if we were to repeat the sampling process and construct multiple intervals, about 95% of those intervals would contain the true population parameter. So, statement I is correct.

II. For a given sample size, 95% of the samples will have the sample statistic for the population parameter lie within the specified confidence interval around the actual population parameter. This statement is incorrect. The confidence interval is constructed around the sample statistic, not the population parameter. The sample statistic is a single value calculated from the sample data, such as a sample mean or proportion. The confidence interval gives us a range of values within which we believe the true population parameter lies. So, statement II is incorrect.

III. The confidence interval will correctly estimate the population parameter with a probability of 95%. This statement is incorrect. A confidence interval provides a range of plausible values for the population parameter, but it does not guarantee that the true parameter lies within that range with a specific probability. The confidence level refers to the long-term performance of the interval estimation procedure, not the probability that a specific interval contains the parameter. So, statement III is incorrect.

Based on the analysis above, the correct answer is:

A. III only