Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q. R10.4 (page 696)

Candles A company produces candles. Machine 1 makes candles with a mean

length of 15cm and a standard deviation of 0.15cm. Machine 2 makes candles with a

mean length of 15cm and a standard deviation of 0.10cm. A random sample of 49

candles is taken from each machine. Let x ̄1−x ̄2 be the

difference (Machine 1 – Machine 2) in the sample mean length of candles. Describe the

shape, center, and variability of the sampling distribution of x ̄1−x ̄2.

Short Answer

Expert verified

Shape: Shape is approximately normal

Center: μx ̄1−x ̄2=0

Variability:σx ̄1−x ̄2=0.026cm

Step by step solution

01

Step 1:Given Information

We have been given that,

Machine 1 :

candles with a mean length,x1= 15cm

candles with a standard deviation,σ1= 0.15cm

random sample of candles (n1)=49

Machine 2:

candles with a mean length,x2= 15cm

candles with a standard deviation,σ2= 0.10cm

random sample of candles (n2)=49

02

Step 2:Explanation

n1 >30 and n2 >30

So, x ̄1−x ̄2 has approximately normal shape.

μx1−x2=x1-x2=15-15=0

So,center =0

Variability:

localid="1654269722311" σx1-x2=σ12n1+σ22n2=localid="1654269775856" 0.15249+0.10249=localid="1654269783223" 0.026cm

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

At a baseball game, 42of 65randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34of 52randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90%confidence interval for the difference (Game − Concert) in population proportions is (−0.154,0.138). Which of the following gives the correct outcome of the researcher’s test of the claim?

a. Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.

b. Because the center of the interval is -0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

c. Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.

d. Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

e. The researcher cannot draw a conclusion about a claim without performing a significance test.

Happy customers As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study interviewed separate random samples of Hispanic and Anglo customers leaving a bank. Customers were classified as Hispanic if they preferred to be interviewed in Spanish or as Anglo if they preferred English. Each customer rated the importance of several aspects of bank service on a 10- point scale.25 Here are summary results for the importance of “reliability” (the accuracy of account records, etc.):

Researchers want to know if there is a difference in the mean reliability ratings of all Anglo and Hispanic bank customers.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check that the conditions for performing the test are met.

Which of the following describes a Type II error in the context of this study?

a. Finding convincing evidence that the true means are different for males and females when in reality the true means are the same

b. Finding convincing evidence that the true means are different for males and females when in reality the true means are different

c. Not finding convincing evidence that the true means are different for males and females when in reality the true means are the same

d. Not finding convincing evidence that the true means are different for males and females when in reality the true means are different

e. Not finding convincing evidence that the true means are different for males and females when in reality there is convincing evidence that the true means are different.

A study of the impact of caffeine consumption on reaction time was designed to correct for the impact of subjects’ prior sleep deprivation by dividing the 24subjects into 12pairs on the basis of the average hours of sleep they had had for the previous 5 nights. That is, the two with the highest average sleep were a pair, then the two with the next highest average sleep, and so on. One randomly assigned member of each pair drank 2cups of caffeinated coffee, and the other drank 2cups of decaf. Each subject’s performance on a Page Number: 690standard reaction-time test was recorded. Which of the following is the correct check of the “Normal/Large Sample” condition for this significance test?

I. Confirm graphically that the scores of the caffeine drinkers could have come from a Normal distribution.

II. Confirm graphically that the scores of the decaf drinkers could have come from a Normal distribution.

III. Confirm graphically that the differences in scores within each pair of subjects could have come from a Normal distribution.

a. I only

b. II only

c. III only

d. I and II only

e. I, I, and III

TicksLyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population, in turn, rises and falls with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. To see if mice are more likely to breed when there are more acorns, the researchers added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54of the 72mice trapped in the first area were in breeding condition, versus 10of the 17mice trapped in the second area.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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