/*! 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} Q43E Suppose the amount of liquid dis... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q43E (page 230)

Suppose the amount of liquid dispensed by a certain machine is uniformly distributed with lower limit \({\rm{A = 8oz}}\) and upper limit\({\rm{B = 10oz}}\). Describe how you would carry out simulation experiments to compare the sampling distribution of the (sample) fourth spread for sample sizes\({\rm{n = 5,10,20}}\), and\({\rm{30}}\).

Short Answer

Expert verified

This yields \({\rm{1000}}\) fourth spreads for each sample size. To compare the sample distributions, use any method to visualize the data. Compare the results of each sample distribution on its own histogram.

Step by step solution

01

Definition

Probability simply refers to the likelihood of something occurring. We may talk about the probabilities of particular outcomes鈥攈ow likely they are鈥攚hen we're unclear about the result of an event. Statistics is the study of occurrences guided by probability.

02

Determining how would carry out simulation experiments

Assume we have a total of \({\rm{n}}\) observations. We define the low fourth as the median of the smallest half and the upper fourth as the median of the biggest half by sorting the observations from smallest to largest and splitting them into two halves (smallest half/largest half; if \({\rm{n}}\) is odd, the median \({\rm{\tilde x}}\) is included in both halves). The fourth spread, \({{\rm{f}}_{\rm{s}}}\), is defined as follows:

\({{\rm{f}}_{\rm{s}}}{\rm{ = upper fourth - lower fourth}}{\rm{. }}\)

The fourth spread contains the statistic of interest. It is simple to calculate the value of the fourth spread given data. We must first simulate the data in order to compare the sampling distribution of the fourth spread for specified sample sizes \({\rm{n = 5,10,20,40}}\).

For example, using a uniform distribution with stated bounds \({\rm{A}}\) and\({\rm{B}}\), use a computer to create samples of the specified sizes. Take the same number of replications for each sample (it does not have to be really big number, \({\rm{1000}}\)should be enough).

Calculate the fourth spread for each replication as follows:

\({{\rm{f}}_{\rm{s}}}{\rm{ = upper fourth - lower fourth}}{\rm{. }}\)

For each sample size, this results in fourth spreads. Use any method to visualize the data to compare the sample distributions. For example, make a distinct histogram for each sample distribution and compare them.

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

There are \({\rm{40}}\) students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of \({\rm{6}}\)min and a standard deviation of \({\rm{6}}\)min.

a. If grading times are independent and the instructor begins grading at \({\rm{6:50}}\) p.m. and grades continuously, what is the (approximate) probability that he is through grading before the \({\rm{11:00}}\) p.m. TV news begins?

b. If the sports report begins at \({\rm{11:10,}}\) what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?

A stockroom currently has \({\rm{30}}\) components of a certain type, of which \({\rm{8}}\) were provided by supplier \({\rm{1,10}}\)by supplier \({\rm{2}}\) , and \({\rm{12}}\) by supplier \({\rm{3}}\). Six of these are to be randomly selected for a particular assembly. Let \({\rm{X = }}\) the number of supplier l's components selected, \({\rm{Y = }}\) the number of supplier \({\rm{2}}\) 's components selected, and \({\rm{p(x,y)}}\) denote the joint pmf of \({\rm{X}}\) and\({\rm{Y}}\).

a. What is \({\rm{p(3,2)}}\) ? (Hint: Each sample of size \({\rm{6}}\) is equally likely to be selected. Therefore, \({\rm{p(3,2) = }}\) (number of outcomes with \({\rm{X = 3}}\) and \({\rm{Y = 2)/(}}\) total number of outcomes). Now use the product rule for counting to obtain the numerator and denominator.)

b. Using the logic of part (a), obtain \({\rm{p(x,y}}\) ). (This can be thought of as a multivariate hypergeometric distribution-sampling without replacement from a finite population consisting of more than two categories.)

Answer

Suppose the proportion of rural voters in a certain state who favor a particular gubernatorial candidate is\(.{\bf{45}}\)and the proportion of suburban and urban voters favouring the candidate is\(.{\bf{60}}\). If a sample of\({\bf{200}}\)rural voters and\({\bf{300}}\)urban and suburban voters is obtained, what is the approximate probability that at least\(\;{\bf{250}}\)of these voters favour this candidate?

Annie and Alvie have agreed to meet between\({\rm{5:00 P}}{\rm{.M}}\). and\({\rm{6:00 P}}{\rm{.M}}\). for dinner at a local health-food restaurant. Let\({\rm{X = }}\)Annie's arrival time and\({\rm{Y = }}\)Alvie's arrival time. Suppose\({\rm{X}}\)and\({\rm{Y}}\)are independent with each uniformly distributed on the interval\({\rm{(5,6)}}\).

a. What is the joint pdf of\({\rm{X}}\)and\({\rm{Y}}\)?

b. What is the probability that they both arrive between\({\rm{5:15}}\)and\({\rm{5:45}}\)?

c. If the first one to arrive will wait only \({\rm{10\;min}}\) before leaving to eat elsewhere, what is the probability that they have dinner at the health-food restaurant? (Hint: The event of interest is\({\rm{A = \{(x,y):|x - y|拢1/6\}}}\).)

A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (\({\rm{1000}}\)s of dollars) is as follows:

\(\begin{array}{*{20}{c}}{{\rm{ Office }}}&{\rm{1}}&{\rm{1}}&{\rm{2}}&{\rm{2}}&{\rm{3}}&{\rm{3}}\\{{\rm{ Employee }}}&{\rm{1}}&{\rm{2}}&{\rm{3}}&{\rm{4}}&{\rm{5}}&{\rm{6}}\\{{\rm{ Salary }}}&{{\rm{29}}{\rm{.7}}}&{{\rm{33}}{\rm{.6}}}&{{\rm{30}}{\rm{.2}}}&{{\rm{33}}{\rm{.6}}}&{{\rm{25}}{\rm{.8}}}&{{\rm{29}}{\rm{.7}}}\end{array}\)

a. Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary\({\rm{\bar X}}\).

b. Suppose one of the three offices is randomly selected. Let\({{\rm{X}}_{\rm{1}}}\)and\({{\rm{X}}_{\rm{2}}}\)denote the salaries of the two employees. Determine the sampling distribution of\({\rm{\bar X}}\).

c. How does \({\rm{E(\bar X)}}\) from parts (a) and (b) compare to the population mean salary\({\rm{\mu }}\)?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.