/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Explain the meaning of a point e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 2

Explain the meaning of a point estimate and an interval estimate.

Short Answer

Expert verified
A point estimate is a single value estimate for a population parameter. The most common point estimate is the mean (average) of a sample. An interval estimate provides a range within which the parameter is estimated to lie, with a certain degree of confidence. This range is computed based on the point estimate and is anchored by a lower and upper value.

Step by step solution

01

Understanding Point Estimate

A point estimate of a population parameter is a single value of a statistic. For example, the sample mean, \( \bar{x} \), is a point estimate of the population mean, \( \mu \). When an estimate is composed of a single value, like a sample mean, it is called a point estimate.
02

Understanding Interval Estimate

An interval estimate is defined as a range of values that鈥檚 likely to contain a population parameter. Interval estimates, also called confidence intervals, offer more information about a population parameter, but they are also less precise. An interval estimate is in the form \( (\bar{x}-E, \bar{x}+E ) \) where \(E\) is the margin of error.
03

Differences between Point and Interval Estimate

The main difference between these two types of estimates lies in the information they provide about the population parameter. A point estimate provides the best single guess while an interval estimate provides a range of plausible values. Another difference is in terms of precision. Point estimates, because they are less precise, are easier to obtain, but they carry a higher risk of being incorrect. On the other hand, interval estimates are more complex to calculate but their range offers a high degree of confidence that the population parameter lies within it.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

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.

At Farmer's Dairy, a machine is set to fill 32 -ounce milk cartons. However, this machine does not put exactly 32 ounces of milk into each carton; the amount varies slightly from carton to carton. It is known that when the machine is working properly, the mean net weight of these cartons is 32 ounces. The standard deviation of the amounts of milk in all such cartons is always equal to \(.15\) ounce. The quality control department takes a sample of 25 such cartons every week, calculates the mean net weight of these cartons, and makes a \(99 \%\) confidence interval for the population mean. If either the upper limit of this confidence interval is greater than \(32.15\) ounces or the lower limit of this confidence interval is less than \(31.85\) ounces, the machine is stopped and adjusted. A recent sample of 25 such cartons produced a mean net weight of \(31.94\) ounces. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the amounts of milk put in all such cartons have a normal distribution.

Check if the sample size is large enough to use the normal distribution to make a confidence interval for \(p\) for each of the following cases. a. \(n=80\) and \(\hat{p}=.85\) b. \(n=110 \quad\) and \(\quad \hat{p}=.98\) c. \(n=35\) and \(\hat{p}=.40\) d. \(n=200\) and \(\hat{p}=.08\)

You are working for a bank. The bank manager wants to know the mean waiting time for all customers who visit this bank. She has asked you to estimate this mean by taking a sample. Briefly explain how you will conduct this study. Collect data on the waiting times for 45 customers who visit a bank. Then estimate the population mean. Choose your own confidence level.

What is the point estimator of the population proportion, \(p ?\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.