Chapter 8, Problem 1RP

Explain the difference between a point estimate of a parameter and a confidence-interval estimate of a parameter.

To determine

Explain the difference between the point estimate and the confidence interval estimate of a parameter.

Explanation of Solution

Confidence Interval:

The confidence interval is the interval estimate of the population parameter. It is the range where the population parameter value will lie in between.

The form of the confidence interval is as follows:

$CI=\text{Point}\text{estimate}\pm \text{Margin}\text{of}\text{error}$

The 95% confidence level means 95% of all the possible sample values within the confidence interval will have the population parameter value and 5% of the sample values within the confidence interval will not have the population parameter.

Point estimate:

Any statistic can be a point estimate which gives the estimated value for the parameter in the population. These estimated values are single values, which come from a set of sample data as an estimator for the population.

Difference:

The point estimate represents the single estimated value for the parameter. If the sample differs, which is for the repeated samples, the point estimate will differ and the estimated value will contradict.

Point estimate does not deal with the accuracy for the statistic to be the parameter.

Whereas a confidence interval gives the interval estimate, therefore, for the repeated samples, the estimate of the parameter will lie in the particular interval for the corresponding confidence level. Mainly, it deals with the accuracy by representing the particular confidence level.