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Chapter 8: Problem 1

Briefly explain the meaning of an estimator and an estimate.

Short Answer

Expert verified
In statistics, an estimator is a rule or a mathematical function for calculating an estimate of a given quantity based on observed data, such as the sample mean for estimating population mean. An estimate is the actual value or statistical conclusion derived from the calculation, for instance, a numerical determination of the population mean based on a given sample set.

Step by step solution

01

Define Estimator

An estimator refers to a rule for calculating an estimate of a given quantity based on observed data. In other words, it is a mathematical function or a formula that combines the data to give an estimate. The key factor to note is that an estimator involves a calculation with data from a sample. For example, the sample mean is an estimator of the population mean.
02

Define Estimate

An estimate, on the other hand, is the result of applying an estimator given a certain data set. This is the actual numerical value obtained from the calculation or the statistical conclusion. For instance, if we have a sample of ages (10, 20, 12, 15, and 17), applying the sample mean estimator, we get an estimate (the actual number) which is 14.8.
03

Contrast Between Estimator and Estimate

Estimator and estimate can be contrasted in terms of function and value. While an estimator is a function, a formula or a rule used, estimate is the value that results from the calculation. The estimator is hypothetical and tells you how to compute an estimate, but the estimate is a number. The estimator remains the same because it's a formula, but the estimate can change, depending on the data.

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Most popular questions from this chapter

You want to estimate the percentage of students at your college or university who are satisfied with the campus food services. Briefly explain how you will make such an estimate. Select a sample of 30 students and ask them whether or not they are satisfied with the campus food services. Then calculate the percentage of students in the sample who are satisfied. Using this information, find the confidence interval for the corresponding population percentage. Select your own confidence level.

For each of the following, find the area in the appropriate tail of the \(t\) distribution. a. \(t=-1.302\) and \(d f=42\) b. \(t=2.797\) and \(n=25\) c. \(t=1.397\) and \(n=9\) d. \(t=-2.383\) and \(d f=67\)

The management of a health insurance company wants to know the percentage of its policyholders who have tried alternative treatments (such as acupuncture, herbal therapy, etc.). A random sample of 24 of the company's policyholders were asked whether or not they have ever tried such treatments. The following are their responses. \(\begin{array}{llllllll}\text { Yes } & \text { No } & \text { No } & \text { Yes } & \text { No } & \text { Yes } & \text { No } & \text { No } \\ \text { No } & \text { Yes } & \text { No } & \text { No } & \text { Yes } & \text { No } & \text { Yes } & \text { No } \\ \text { No } & \text { No } & \text { Yes } & \text { No } & \text { No } & \text { No } & \text { Yes } & \text { No }\end{array}\) a. What is the point estimate of the corresponding population proportion? b. Construct a \(99 \%\) confidence interval for the percentage of this company's policyholders who have tried alternative treatments.

A consumer agency wants to estimate the proportion of all drivers who wear seat belts while driving. Assume that a preliminary study has shown that \(76 \%\) of drivers wear seat belts while driving. How large should the sample size be so that the \(99 \%\) confidence interval for the population proportion has a margin of error of \(.03\) ?

Determine the most conservative sample size for the estimation of the population proportion for the following. a. \(E=.025\), confidence level \(=95 \%\) b. \(E=.05, \quad\) confidence level \(=90 \%\) c. \(E=.015\), confidence level \(=99 \%\)
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