Chapter 7, Problem 1CRP

To determine

Define the term point estimate.

Define the term critical value.

Define the term maximal margin of error.

Define the term confidence level.

Define the term confidence interval.

Explanation of Solution

Point estimate:

The estimate of the parameter value based on single number is referred as point estimate. For example $\overline{x}$ is the point estimate for $\mu$, $\widehat{p}$ is point estimate for p.

Critical value:

The critical value is the area between two specified values under probability distribution curve. For a confidence level c the cut-off area for c is obtained using critical value. For instance consider standard normal distribution.

The critical value is the area between $-z_c\text{and}{z}_c$ under the standard normal curve. That is, for confidence level c, the number of standard deviations on both sides of the mean is obtained from the standard normal table by using the central area c under standard normal curve.

Maximal margin of error:

Under certain circumstances the largest difference (or error) between the point estimate and the population parameter is referred as maximal margin of error. It is denoted by symbol E and is the half-width of a confidence interval.

Confidence level:

The measure of reliability for estimating the interval is referred as confidence level. It is denoted by symbol c. The value c is the proportion of calculated confidence intervals that would include the population parameter that is being estimated in the study. It cannot be considered as the measure of reliability for a single interval.

Confidence interval:

Confidence interval gives the interval estimates of the parameter being estimated. That is, the confidence interval determines the range for the parameter value. If c% confidence interval is considered then, if repeated samples of size n are drawn then c% confidence intervals contain the true parameter value.