Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q64E (page 452)

Enough money has been budgeted to collect independent random samples of size n1=n2=100from populations 1 and 2 to estimate localid="1664867109106" μ1-μ2. Prior information indicates that σ1=σ2=10. Have sufficient funds been allocated to construct a 90% confidence interval forμ1-μ2of width 5 or less? Justify your answer.

Short Answer

Expert verified

The required sample size is 22. Since, the sample size for each population is large enough.

Step by step solution

01

Given Information

The sample size of two populations are given below

n1=n2=100

The standard deviation of two populations are given below

σ1=σ2=10

The sampling error is

SE=5

02

Z-value

For α=0.1

The z-value is given by

zα2=z0.05=1.645

03

Compute the sample

For, z=1.645,σ1=σ2=10 andSE=5

The sample is calculated as

n1=n2=z0.052×σ12+σ22SE2=1.6452×102+10252=2.7060×20025=541.225=21.648≈22

Therefore, the required sample size is 22.

Since, the sample size for each population is large enough.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Given that xis a hypergeometric random variable, computep(x)for each of the following cases:

a. N= 8, n= 5, r= 3, x= 2

b. N= 6, n= 2, r= 2, x= 2

c. N= 5, n= 4, r= 4, x= 3

The “last name” effect in purchasing. The Journal of Consumer Research (August 2011) published a study demonstrating the “last name” effect—i.e., the tendency for consumers with last names that begin with a later letter of the alphabet to purchase an item before consumers with last names that begin with earlier letters. To facilitate the analysis, the researchers assigned a number, x, to each consumer based on the first letter of the consumer’s last name. For example, last names beginning with “A” were assigned x = 1; last names beginning with “B” were assigned x = 2; and last names beginning with “Z” were assigned x = 26.

a. If the first letters of consumers’ last names are equally likely, find the probability distribution for x.

b. Find E (x) using the probability distribution, part a. If possible, give a practical interpretation of this value.?

c. Do you believe the probability distribution, part a, is realistic? Explain. How might you go about estimating the true probability distribution for x

A paired difference experiment yielded ndpairs of observations. In each case, what is the rejection region for testing H0:μd>2?

a. nd=12,α=.05

b.nd=24,α=.10

c.nd=4,α=.025

d.nd=80,α=.01

The gender diversity of a large corporation’s board of directors was studied in Accounting & Finance (December 2015). In particular, the researchers wanted to know whether firms with a nominating committee would appoint more female directors than firms without a nominating committee. One of the key variables measured at each corporation was the percentage of female board directors. In a sample of 491firms with a nominating committee, the mean percentage was 7.5%; in an independent sample of 501firms without a nominating committee, the mean percentage was role="math" localid="1652702402701" 4.3% .

a. To answer the research question, the researchers compared the mean percentage of female board directors at firms with a nominating committee with the corresponding percentage at firms without a nominating committee using an independent samples test. Set up the null and alternative hypotheses for this test.

b. The test statistic was reported as z=5.1 with a corresponding p-value of 0.0001. Interpret this result if α=0.05.

c. Do the population percentages for each type of firm need to be normally distributed for the inference, part b, to be valid? Why or why not?

d. To assess the practical significance of the test, part b, construct a 95% confidence interval for the difference between the true mean percentages at firms with and without a nominating committee. Interpret the result.

Question: The purpose of this exercise is to compare the variability of with the variability of .

a. Suppose the first sample is selected from a population with mean and variance . Within what range should the sample mean vary about of the time in repeated samples of measurements from this distribution? That is, construct an interval extending standard deviations of on each side of .

b. Suppose the second sample is selected independently of the first from a second population with mean and variance . Within what range should the sample mean vary about the time in repeated samples of measurements from this distribution? That is, construct an interval extending standard deviations on each side .

c. Now consider the difference between the two sample means . What are the mean and standard deviation of the sampling distribution ?

d. Within what range should the difference in sample means vary about the time in repeated independent samples of measurements each from the two populations?

e. What, in general, can be said about the variability of the difference between independent sample means relative to the variability of the individual sample means?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.

Sign-up for free