An interval estimate is a range of values in which the population parameter is likely to occur

Point estimate and Interval estimates are the two forms of population parameter estimation based on sample data. Point estimation is very easy to compute. However, interval estimate is a much more robust and practical approach than the point estimate.

What is an Estimation?

Estimation is a process in which we obtain the values of unknown population parameters with the help of sample data. In other words, it is a data analysis framework that uses a combination of effect sizes, confidence intervals to plan an experiment, analyze data and interpret the results.

Furthermore, the basic purpose of estimating methods is to estimate the size of an effect and report the effect size along with its confidence interval.

The estimator is a method, formula, or function that specifically tells how to compute an estimate. In other words, to estimate the value of the population parameter, you can use information from the sample in the form of an estimator.

Properties of Estimators

Sample measures are used to estimate the population measures; these statistics are the estimators. Following are the properties of good estimators.

• An estimator should be consistent. For instance, if it is consistent, the estimator value approaches the parameter value estimated as the sample size increases.
• Estimators should be unbiased. In other words, the expected value obtained from the sample is equal to the parameter being estimated. Otherwise, the estimator is biased.
• The estimator should be efficient. In other words, it should have minimal variance to the actual variance of the estimator.

Variables

• x: The individual value
• X̅: a point estimate for the population mean
• σ: the actual population standard deviation / symbol for the measurement of dispersion in a population
• n: The statistic for number of data in a sample
• N is for populations
• X̿:(double bar): The grand average of the subgroup averages. AKA X-bar bar or X-double bar
• s (or sd): The sample standard deviation is a point estimate for the population standard deviation / the dispersion statistic for samples
• µ: the central tendency statistic for populations

Also see types of statistics

Types of Estimation

Estimators are two different types

• Point Estimates
• Interval Estimates

Point Estimates

A point estimate is a sample statistic calculated using the sample data to estimate the most likely value of the corresponding unknown population parameter. In other words, point estimate is a single value derived from a sample and used to estimate the population value.

For instance, if we use a value of x̅ to estimate the mean µ of a population.

x̅ = Σx/n

For example, 62 is the average (x̅) marks achieved by a sample of 15 students randomly collected from a class of 150 students is considered to be the mean marks of the entire class. Since it is in the single numeric form, it is a point estimator.

The basic drawback of point estimate is that no information is available regarding the reliability. In fact, the probability that a single sample statistic is equal to the population parameter is very less.

Take a sample, find x̅. x̅ is a close approximation of μ. But, depending on the size of your sample that may not be a good point estimate. s is a good approximation of σ. So, if we want stronger confidence in what range our estimate lies, we need to do a confidence interval.

Interval Estimates

A confidence interval estimate is a range of values constructed from sample data so that the population parameter is likely to occur within the range at a specified probability. The specified probability is the level of confidence.

• Broader and probably more accurate than a point estimate
• Used with inferential statistics to develop a confidence interval – where we believe with a certain degree of confidence that the population parameter lies.
• Any parameter estimate that is based on a sample statistic has some amount of sampling error.

In statistics, interval estimation is the use of sample data to calculate an interval of possible values of an unknown population parameter.

Below are the factors that determine the width of a confidence level

• Sample size
• Population variability
• Desired level of confidence

Confidence Interval

Confidence interval is to express the precision and ambiguity related to a particular sampling method. Additionally, the confidence interval equation consists of 3 parts.

A confidence interval is a range of values that probably contain the population mean.

Confidence level is a percentage of certainty that in any given sample, that confidence interval will contain the population mean.

Point estimate is a statistic (value from a sample) is to estimate a parameter (value from the population).

Margin of error is the maximum expected difference between the actual population parameter and a sample estimate of the parameter. In other words, it is the range of values above and below sample statistics.

Interval Estimates Examples

Example 1:

A large company conducted a series of tests to determine how much data individual users were storing on the file server. So, a random sample of 15 users revealed an average 15.32 GB with a standard deviation of 0.18 GB. What is the interval that contains the actual company user average?

Example 2:

A plastic injection molding company is trying out a new die. So, based on a sample of 25 trials, the average cycle time was 7.49 seconds with a standard deviation of 0.22 seconds. However, this machine known process variance is 0.0576. Find the confidence limits of µ. Test at the 99% confidence level.

Example 3:

The mean length of the 25 parts plastic injection molding process is 4.32 cm with a standard deviation of 0.17 cm. What is the 95% confidence interval for the actual mean of this process?

Point and Interval Estimation Videos

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  What is an interval estimate of a population parameter?

  interval estimation, in statistics, the evaluation of a parameter—for example, the mean (average)—of a population by computing an interval, or range of values, within which the parameter is most likely to be located.

  What is an interval estimate used to estimate?

  A point estimate is a single value estimate of a parameter. For instance, a sample mean is a point estimate of a population mean. An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.

  Does an interval estimate always contains the population parameter?

  Answer and Explanation: TRUE. The point estimate of a population parameter is always at the center of the confidence interval for the parameter.

  Why is the interval estimate a preferred value for the population parameter?

  Interval estimation is the range of estimation that has a pleasant chance to contain the population parameter. It is technically preferred over point estimates because: It includes the range of estimates that will contain the population parameter.