/*! 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} Q-8-1E Question: The purpose of this ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q-8-1E (page 465)

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?

Short Answer

Expert verified

Answer

The standard deviation is a statistic that calculates the square root of the variance as well as quantifies the dispersal of a collection compared to its average.

Step by step solution

01

Central Limit Theorem. 

According to theCentral Limit Theorem,the sampling distribution of the sample means approaches a normal distribution, irrespective of the shape of population distribution if the sample size is over 30.

02

(a) Find the interval extending 2 standard deviations x1¯on each sideμ1

d

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

To compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:

Sample 1

Sample 2

x炉1=5,275蟽1=150

x炉2=5,240蟽2=200

a. Use a 95%confidence interval to estimate the difference between the population means (渭1鈭�渭2). Interpret the confidence interval.

b. Test the null hypothesis H0:(渭1鈭�渭2)=0versus the alternative hypothesis Ha:(渭1鈭�渭2)鈮�0 . Give the significance level of the test and interpret the result.

c. Suppose the test in part b was conducted with the alternative hypothesis Ha:(渭1鈭�渭2)鈮�0 . How would your answer to part b change?

d. Test the null hypothesis H0:(渭1鈭�渭2)=25 versus Ha:(渭1鈭�渭2)鈮�25. Give the significance level and interpret the result. Compare your answer with the test conducted in part b.

e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a鈥揹?

Last name and acquisition timing. Refer to the Journal of Consumer Research (August 2011) study of the last name effect in acquisition timing, Exercise 8.13 (p. 466). Recall that the mean response times (in minutes) to acquire free tickets were compared for two groups of MBA students鈥� those students with last names beginning with one of the first nine letters of the alphabet and those with last names beginning with one of the last nine letters of the alphabet. How many MBA students from each group would need to be selected to estimate the difference in mean times to within 2 minutes of its true value with 95% confidence? (Assume equal sample sizes were selected for each group and that the response time standard deviation for both groups is 蟽鈮� 9 minutes.)

Whistle-blowing among federal employees. Whistle blowing refers to an employee鈥檚 reporting of wrongdoing by co-workers. A survey found that about 5% of employees contacted had reported wrongdoing during the past 12 months. Assume that a sample of 25 employees in one agency are contacted and let x be the number who have observed and reported wrongdoing in the past 12 months. Assume that the probability of whistle-blowing is .05 for any federal employee over the past 12 months.

a. Find the mean and standard deviation of x. Can x be equal to its expected value? Explain.

b. Write the event that at least 5 of the employees are whistle-blowers in terms of x. Find the probability of the event.

c. If 5 of the 25 contacted have been whistle-blowers over the past 12 months, what would you conclude about the applicability of the 5% assumption to this

agency? Use your answer to part b to justify your conclusion.

A paired difference experiment produced the following results:

nd=38,x炉1=92,x炉2=95.5,d炉=-3.5,sd2=21

a. Determine the values zfor which the null hypothesis 渭1鈭�渭2=0would be rejected in favor of the alternative hypothesis 渭1鈭�渭2<0 Use .role="math" localid="1652704322912" 伪=.10

b. Conduct the paired difference test described in part a. Draw the appropriate conclusions.

c. What assumptions are necessary so that the paired difference test will be valid?

d. Find a90% confidence interval for the mean difference 渭d.

e. Which of the two inferential procedures, the confidence interval of part d or the test of the hypothesis of part b, provides more information about the differences between the population means?

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
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics 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.