/*! 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 The Orangetown Medical Research ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 2

The Orangetown Medical Research Center randomly selects 100 births in the United States each day, and the proportion of boys is recorded for each sample. a. Do you think the births are randomly selected with replacement or without replacement? b. Give two reasons why statistical methods tend to be based on the assumption that sampling is conducted with replacement, instead of without replacement.

Short Answer

Expert verified
a. Sampling is done with replacement. b. It ensures independence of selections and maintains consistent probabilities.

Step by step solution

01

Title - Understanding Sampling Method

First, consider the nature of the sampling process. When taking samples from a large population without replacement, each member is only considered once. In contrast, with replacement, members can be chosen more than once. Since 100 births are selected each day across the entire country, it implies a large population and a practical ease to operate with replacement.
02

Title - Deciding the Sampling Method

Due to the vast number of births each day, selecting the same birth more than once would likely be almost impossible. Therefore, it can be reasonably concluded that sampling is done with replacement.
03

Title - Reason 1 for Using Replacement

Statistical methods prefer sampling with replacement because it ensures each selection is independent of others. This independence simplifies the mathematical calculations and models used to analyze the data.
04

Title - Reason 2 for Using Replacement

Another reason for using replacement is that it allows for a consistent probability of selecting any member of the population in each draw. This consistency helps in maintaining the sampling distribution's properties and robustness of statistical inference.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

sampling with replacement
When sampling is done with replacement, each chosen element is returned to the population before the next draw. This means that every selection is independent and does not alter the makeup of the population.

Consider the example of selecting 100 births from the United States each day. Because the population from which the births are selected is so large, it's as if the sampling is done with replacement. This simplifies the sampling process and makes it more manageable.

Sampling with replacement is beneficial because it ensures that each birth has an equal chance of being chosen, maintaining the randomness and fairness of the process.
independence in sampling
Independence in sampling means that the selection of one sample does not influence the selection of another. This concept is closely linked to sampling with replacement since returning each sample to the population ensures that future selections remain unaffected.

For example, if the Orangetown Medical Research Center selects 100 births with replacement, the chance of selecting a particular birth remains stable for each draw. This independence simplifies statistical calculations.
  • Ensures consistency and reliability in results
  • Makes mathematical models easier to apply
sampling distribution
A sampling distribution refers to the probability distribution of a statistic (like a sample mean or proportion) obtained from a large number of samples drawn from a population.

When the Orangetown Medical Research Center records the proportion of boys from their daily samples, they can build a sampling distribution by analyzing these proportions over time.

Random sampling with replacement helps maintain the properties of this distribution, ensuring accurate and reliable statistical inferences. This is important for:
  • Estimating population parameters
  • Formulating predictions and decisions

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

A common design requirement is that an environment must fit the range of people who fall between the 5 th percentile for women and the 95 th percentile for men. In designing an assembly work table, we must consider sitting knee height, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of \(21.4\) in. and a standard deviation of \(1.2\) in.; females have sitting knee heights that are normally distributed with a mean of \(19.6\) in. and a standard deviation of \(1.1\) in. (based on data from the Department of Transportation). a. What is the minimum table clearance required to satisfy the requirement of fitting \(95 \%\) of men? Why is the 95 th percentile for women ignored in this case? b. The author is writing this exercise at a table with a clearance of \(23.5\) in. above the floor. What percentage of men fit this table, and what percentage of women fit this table? Does the table appear to be made to fit almost everyone?

Do the following: If the requirements of \(n p \geq 5\) and \(n q \geq 5\) are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if \(n p<5\) or \(n q<5\), then state that the normal approximation should not be used. With \(n=20\) guesses and \(p=0.2\) for a correct answer, find \(P(\) at least 6 correct answers \()\).

Data Set 4 "Births" in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median; sample range; sample variance; sample standard deviation; sample proportion?

A normal distribution is informally described as a probability distribution that is bell-shaped when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.

Use these parameters (based on Data Set 1 "Body Data" in Appendix B): \- Men's heights are normally distributed with mean \(68.6 \mathrm{in.}\) and standard deviation \(2.8 \mathrm{in} .\) \- Women's heights are normally distributed with mean 63.7 in. and standard deviation \(2.9 \mathrm{in}\). The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of \(51.6 \mathrm{in}\). a. What percentage of adult men can fit through the door without bending? b. Does the door design with a height of \(51.6\) in. appear to be adequate? Why didn't the engineers design a larger door? c. What doorway height would allow \(40 \%\) of men to fit without bending?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.